#include<bits/stdc++.h>
#define rep(i,start,lim) for(lld i=start;i<lim;i++)
#define repd(i,start,lim) for(lld i=start;i>=lim;i--)
#define scan(x) scanf("%lld",&x)
#define print(x) printf("%lld ",x)
#define f first
#define s second
#define pb push_back
#define mp make_pair
#define br printf("\n")
#define sz(a) lld((a).size())
#define YES printf("YES\n")
#define NO printf("NO\n")
#define all(c) (c).begin(),(c).end()
#define INF         1011111111
#define LLINF       1000111000111000111LL
#define EPS         (double)1e-10
#define MOD         1000000007
#define PI          3.14159265358979323
using namespace std;
typedef long double ldb;
typedef long long lld;
lld powm(lld base,lld exp,lld mod=MOD) {lld ans=1;while(exp){if(exp&1) ans=(ans*base)%mod;exp>>=1,base=(base*base)%mod;}return ans;}
lld ctl(char x,char an='a') {return (lld)(x-an);}
char ltc(lld x,char an='a') {return (char)(x+an);}
#define bit(x,j) ((x>>j)&1)
typedef vector<lld> vlld;
typedef pair<lld,lld> plld;
typedef map<lld,lld> mlld;
typedef set<lld> slld;
#define sync ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define mxm(a,b) a = max(a,b)
#define mnm(a,b) a = min(a,b)
#define endl '\n'
#define fre freopen("1.in","r",stdin); freopen("1.out","w",stdout);
#define N 1000005
int main()
{
    //sync;
    string s;
    map<char,lld> m;
    cin>>s;
    lld k = sz(s);
    string tmp = "";
    tmp += s[0];
    rep(i,1,k) if(s[i]!=s[i-1]) tmp+=s[i];
    rep(i,0,k) m[s[i]]++;
    if(tmp != "abc") return 0*NO;
    if(m['c']!=m['a'] and m['c']!=m['b']) return 0*NO;
    if(m['a']>=1 and m['b']>=1) return 0*YES;
    else return 0*NO;
    return 0;
}

#include<bits/stdc++.h>
using namespace std;

typedef long long ll;

priority_queue<ll> pq;

int main(){
    int n, k1, k2, k;
    cin>>n>>k1>>k2;
    k = k1+k2;
    vector<ll> a(n), b(n), arr(n);
    for(int i=0 ; i<n ; ++i)
        cin>>a[i];
    for(int i=0 ; i<n ; ++i){
        cin>>b[i];
        arr[i] = abs(a[i]-b[i]);
        pq.push(arr[i]);
    }
    while(k>0){
        ll curr = pq.top();
        pq.pop();
        pq.push(abs(curr-1));
        k--;
    }
    ll ans = 0;
    while(!pq.empty()){
        ll curr = pq.top();
        ans += (curr*curr);
        pq.pop();
    }
    cout<<ans;
}

#include<bits/stdc++.h>
#define rep(i,start,lim) for(lld i=start;i<lim;i++)
#define repd(i,start,lim) for(lld i=start;i>=lim;i--)
#define scan(x) scanf("%lld",&x)
#define print(x) printf("%lld ",x)
#define f first
#define s second
#define pb push_back
#define mp make_pair
#define br printf("\n")
#define sz(a) lld((a).size())
#define YES printf("YES\n")
#define NO printf("NO\n")
#define all(c) (c).begin(),(c).end()
#define INF         1011111111
#define LLINF       1000111000111000111LL
#define EPS         (double)1e-10
#define MOD         1000000007
#define PI          3.14159265358979323
using namespace std;
typedef long double ldb;
typedef long long lld;
lld powm(lld base,lld exp,lld mod=MOD) {lld ans=1;while(exp){if(exp&1) ans=(ans*base)%mod;exp>>=1,base=(base*base)%mod;}return ans;}
lld ctl(char x,char an='a') {return (lld)(x-an);}
char ltc(lld x,char an='a') {return (char)(x+an);}
#define bit(x,j) ((x>>j)&1)
typedef vector<lld> vlld;
typedef pair<lld,lld> plld;
typedef map<lld,lld> mlld;
typedef set<lld> slld;
#define sync ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define mxm(a,b) a = max(a,b)
#define mnm(a,b) a = min(a,b)
#define endl '\n'
#define fre freopen("1.in","r",stdin); freopen("1.out","w",stdout);
#define N 1000005
int main()
{
    //sync;
    lld x,d;
    vector<lld> ans;
    cin>>x>>d;
    lld num = 1, cnt = 0;
    repd(i,60,1) if(bit(x,i)) {
        rep(j,0,i) ans.pb(num);
        cnt++;
        num+=(d+1);
    }
    while(cnt--) ans.pb(num),num+=(d+1);
    if(x%2) ans.pb(num);
    cout<<sz(ans)<<endl;
    for(auto i:ans) cout<<i<<" ";
    return 0;
}

//Gvs Akhil (Vicennial)
#include<bits/stdc++.h>
#define int long long
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define ld(a) while(a--)
#define tci(v,i) for(auto i=v.begin();i!=v.end();i++)
#define tcf(v,i) for(auto i : v)
#define all(v) v.begin(),v.end()
#define rep(i,start,lim) for(long long (i)=(start);i<(lim);i++)
#define sync ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define osit ostream_iterator
#define INF 		0x3f3f3f3f
#define LLINF       1000111000111000111LL
#define PI 			3.14159265358979323
#define endl '\n'
#define trace1(x)                cerr<<#x<<": "<<x<<endl
#define trace2(x, y)             cerr<<#x<<": "<<x<<" | "<<#y<<": "<<y<<endl
#define trace3(x, y, z)          cerr<<#x<<":" <<x<<" | "<<#y<<": "<<y<<" | "<<#z<<": "<<z<<endl
#define trace4(a, b, c, d)       cerr<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<endl
#define trace5(a, b, c, d, e)    cerr<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<" | "<<#e<< ": "<<e<<endl
#define trace6(a, b, c, d, e, f) cerr<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<" | "<<#e<< ": "<<e<<" | "<<#f<<": "<<f<<endl
const int N=1000006;
using namespace std;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef long long ll;
typedef vector<long long> vll;
typedef vector<vll> vvll;
typedef long double ld;
typedef pair<int,int> ii;
typedef vector<ii> vii;
typedef vector<vii> vvii;
typedef tuple<int,int,int> iii;
typedef set<int> si;
typedef complex<double> pnt;
typedef vector<pnt> vpnt;
typedef priority_queue<ii,vii,greater<ii> > spq;
const ll MOD=1000000007LL;
template<typename T> T gcd(T a,T b){if(a==0) return b; return gcd(b%a,a);}
template<typename T> T power(T x,T y,ll m=MOD){T ans=1;while(y>0){if(y&1LL) ans=(ans*x)%m;y>>=1LL;x=(x*x)%m;}return ans%m;}
int shift[66];
inline int getlev(int x){
	int z=__builtin_clzll(x);
	return 64-z;
}
inline int getmod(int x){
	return (1LL<<(x-1));
}
void addshift(int x,int k){
	int m=getmod(x);
	if(k>=m) k%=m;
	shift[x]+=k;
	if(shift[x]>=m) shift[x]-=m;
	if(shift[x]<0) shift[x]+=m;	
}
int getorig(int V,int l){
	int fval=(1LL<<(l-1)); // 2^(L-1)
	int mod=getmod(l);
	int P= V-fval; 
	int Z= fval+((P-shift[l])%mod + mod)%mod;
	return Z;
}
int32_t main(){
	sync;
	int q; cin>>q;
	while(q--){
		int t,x,k;
		cin>>t>>x;
		int l=getlev(x);
		if(t==1){ 
			cin>>k; k%=getmod(l);
			addshift(l,k);
		}
		else if(t==2){// propogating
			cin>>k; 
			k%=getmod(l);
			if(k<0) k+=getmod(l);
			 int curr=1;
			for(int i=l;i<=60;i++){
				addshift(i,k*curr);
				curr<<=1;
			}
		}
		else{ // printing
			int P= x - (1LL<<(l-1)); // Finding index in array
			int V= (1LL<<(l-1)) + ((P+shift[l])%(1LL<<(l-1)) + (1LL<<(l-1)) )%(1ll<<(l-1)); //Finding original value at the new index of X after performing the shift.
			for(int i=l;i>=1;i--){
				int Z = getorig(V,i); // Finding the current value
				cout<<Z<<" "; // printing the current value
				V>>=1; // dividing the original value by 2 to get its parent value
			}
			cout<<endl;
		}
	}
}

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int M=1000005,mod=1e9+7;
vector<int> adj[M];
int par[M],lev[M];
ll v[M];
ll e[M],o[M];
ll ans,res,n;
ll powmod(ll base, ll exponent)
{ 
	//cout<<base<<" "<<exponent<<endl;

	ll ans=1;
	
		while(exponent)
		{ 
			while(exponent%2==0)
			{
				base=(base*base)%mod;
				exponent/=2;
			}
			
			exponent--;
			ans=(ans*base)%mod;
		}
		
	return ans;
}
void dfs(int x,int depth)
{
	//o[x]++;

	lev[x]=depth;
	
	int cno=0;

	for(int i=0;i<adj[x].size();i++)
	{
		int c=adj[x][i];
	
		if(c!=par[x])
		{
			par[c]=x;
	
			dfs(c,depth+1);
		
			if(cno>0)
			{
				ans=( (ans+ 2*( o[x]*e[c]%mod - e[x]*o[c]%mod + mod)%mod*v[x]%mod)+mod )%mod;
			}
			
			cno++;
		
			o[x]+=e[c];
			e[x]+=o[c];
		
		}
	
	}
	
	o[x]++;

	
}
int main()
{
	//freopen("o.out","r",stdin);

	cin>>n;
	
	for(int i=1;i<=n;i++)
	{
		cin>>v[i];
	}
	
	for(int i=1;i<n;i++)
	{
		int u,v;
		
		cin>>u>>v;
		
		adj[u].push_back(v);
		adj[v].push_back(u);
	}
	
	dfs(1,0); 
	
	//cout<<ans<<endl;
	
	for(int i=1;i<=n;i++)
	{	
		//cout<<"###"<<i<<endl;
		if(lev[i]%2)
		{
			ans=((ans+2*(o[i]*(e[1]-o[i]+1)%mod - e[i]*(o[1]-e[i])%mod +mod)%mod*v[i]%mod)%mod+mod )%mod;
		}
		else
		{
			ans=((ans+2*(o[i]*(o[1]-o[i]+1)%mod - e[i]*(e[1]-e[i])%mod +mod)%mod*v[i]%mod)%mod+mod )%mod;
		}
		
		//cout<<ans<<endl;
		
		ans=((ans-v[i])%mod+mod)%mod;
		
//		cout<<i<<" "<<ans<<endl;
		//cout<<ans<<endl;
	}
	
	cout<<ans<<endl;

}

#include <bits/stdc++.h>
using namespace std;
vector<map<int,int> > s;
int getedgelen(int a, int w)
{
    auto it = s[a].lower_bound(w);
    if(it == s[a].begin()) return 1;
    it--;
    return (it->second)+1;
}
int32_t main() {
    ios::sync_with_stdio(false);cin.tie(0);
    int n,m,a,b,w;
    cin>>n>>m;
    s.resize(n+1);
    int ans = 0;
    while(m--)
    {
        cin>>a>>b>>w;
        int val = getedgelen(a,w);
        if(getedgelen(b,w+1) > val)
            continue;
        s[b][w] = max(s[b][w],val);
        auto it = s[b].upper_bound(w);
        while(!(it==s[b].end() || it->second > val))
        {
            it = s[b].erase(it);
        }
        ans = max(ans,val);
    }
    cout<<ans;
    return 0;
}

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pb push_back
const int mod = 998244353;
const int root = 15311432;
const int root_1 = 469870224;
const int root_pw = 1 << 23;
const int N = 400004;

vector<int> v[N];

ll modInv(ll a, ll mod = mod){
	ll x0 = 0, x1 = 1, r0 = mod, r1 = a;
	while(r1){
		ll q = r0 / r1;
		x0 -= q * x1; swap(x0, x1);
		r0 -= q * r1; swap(r0, r1);
	}
	return x0 < 0 ? x0 + mod : x0;
}

void fft (vector<int> &a, bool inv) {
	int n = (int) a.size();

	for (int i=1, j=0; i<n; ++i) {
		int bit = n >> 1;
		for (; j>=bit; bit>>=1)
			j -= bit;
		j += bit;
		if (i < j)
			swap (a[i], a[j]);
	}

	for (int len=2; len<=n; len<<=1) {
		int wlen = inv ? root_1 : root;
		for (int i=len; i<root_pw; i<<=1)
			wlen = int (wlen * 1ll * wlen % mod);
		for (int i=0; i<n; i+=len) {
			int w = 1;
			for (int j=0; j<len/2; ++j) {
				int u = a[i+j],  v = int (a[i+j+len/2] * 1ll * w % mod);
				a[i+j] = u+v < mod ? u+v : u+v-mod;
				a[i+j+len/2] = u-v >= 0 ? u-v : u-v+mod;
				w = int (w * 1ll * wlen % mod);
			}
		}
	}

	if(inv) {
		int nrev = modInv(n, mod);
		for (int i=0; i<n; ++i)
			a[i] = int (a[i] * 1ll * nrev % mod);
	}
}

void pro(const vector<int> &a, const vector<int> &b, vector<int> &res) {
	vector<int> fa(a.begin(), a.end()),  fb(b.begin(), b.end());
	int n = 1;
	while (n < (int) max(a.size(), b.size()))  n <<= 1;
	n <<= 1;
	fa.resize (n),  fb.resize (n);

	fft(fa, false), fft (fb, false);
	for (int i = 0; i < n; ++i)
		fa[i] = 1LL * fa[i] * fb[i] % mod;
	fft (fa, true);
	res = fa;
}

int S(int n, int r) {

	int nn = 1;
	while(nn < n) nn <<= 1;

	for(int i = 0; i < n; ++i) {
		v[i].push_back(i);
		v[i].push_back(1);
	}
	for(int i = n; i < nn; ++i) {
		v[i].push_back(1);
	}

	for(int j = nn; j > 1; j >>= 1){
		int hn = j >> 1;
		for(int i = 0; i < hn; ++i){
			pro(v[i], v[i + hn], v[i]);
		}
	}

	return v[0][r];
}

int fac[N], ifac[N], inv[N];

void prencr(){
	fac[0] = ifac[0] = inv[1] = 1;
    for(int i = 2; i < N; ++i)
    	inv[i] = mod - 1LL * (mod / i) * inv[mod % i] % mod;
    for(int i = 1; i < N; ++i){
    	fac[i] = 1LL * i * fac[i - 1] % mod;
    	ifac[i] = 1LL * inv[i] * ifac[i - 1] % mod;
    }
}

int C(int n, int r){
	return (r >= 0 && n >= r) ? (1LL * fac[n] * ifac[n - r] % mod * ifac[r] % mod) : 0;
}

int main(){
	prencr();
	int n, p, q;
	cin >> n >> p >> q;
	ll ans = C(p + q - 2, p - 1);
	ans *= S(n - 1, p + q - 2);
	ans %= mod;
	cout << ans;
}

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pb push_back
const int N = 400004;

int n;
vector<int> e[N];
int sz[N], par[N], sp[30][N];
int V[N], L[N], CS[N];
bool mark[N];

struct tri {
	long long A, B;
	int C;
};

map<int, tri> nmp[N];

long long D[N]; // Sum of Distances
long long S[N]; // Sum of Depth
int T[N]; // Count

//======================================PRE-PROCESS=========================================

void getLevel(int u, int p = -1){
	sp[0][u] = p;
	for(auto x : e[u]) if(x != p) {
		L[x] = 1 + L[u];
		getLevel(x, u);
	}
}

void prepAncestor(){
	for(int i = 1; (1 << i) <= n; ++i) {
		for(int j = 1; j <= n; ++j) {
			sp[i][j] = sp[i - 1][sp[i - 1][j]];
		}
	}
}

int dist(int u, int v){
	if(L[u] < L[v]) swap(u, v);
	int lgn = 0;
	while((1 << lgn) < n) lgn++;
	int ans = 0;
	for(int i = lgn; i >= 0; --i){
		if(L[u] - (1 << i) >= L[v]){
			u = sp[i][u];
			ans += (1 << i);
		}
	}
	if(u == v) return ans;
	for(int i = lgn; i >= 0; --i){
		if(sp[i][u] != sp[i][v]){
			ans += 1 << (i + 1);
			u = sp[i][u];
			v = sp[i][v];
		}
	}
	return ans + 2;
}

//=================================CENTROID DECOMPOSITION===================================

void getSize(int u, int p = -1) {
      sz[u] = 1;
      for(auto v : e[u]) if(v != p && !mark[v]) {
            getSize(v, u);
            sz[u] += sz[v];
      }
}
 
int getCentroid(int u, int p, int lim) {
      for(auto v : e[u]) if(v != p && !mark[v] && sz[v] > lim) {
            return getCentroid(v, u, lim);
      }
      return u;
}

void decompose(int u, int p = -1) {
      getSize(u);
      int cen = getCentroid(u, -1, sz[u] / 2);
      par[cen] = p == -1 ? cen : p;
      mark[cen] = true;
       
      for(auto v : e[cen]) if(v != p && !mark[v]) {
            decompose(v, cen);
      }
}

//==========================================QUERY-HANDLER===============================================

void updAns(int u, int add) {

	int Z = V[u];
	
	tri tY = nmp[u][Z];
	ll ret = tY.A;
	int y = u, x = par[u];
	while(y != x) {
		tri tX = nmp[x][Z];
		ret += 1LL * (tX.C - tY.C) * dist(x, u) + (tX.A - tY.B);
		y = x;
		tY = tX;
		x = par[x];
	}
	ret <<= 1;

	int mul = add ? 1 : -1;
	D[Z] += mul * ret;
	S[Z] += mul * L[u];
	T[Z] += mul;
}

void updTree(int u, bool add) {
	int Z = V[u];
	int mul = add ? 1 : -1;
	for(int x = u; ; x = par[x]) {
		tri &tX = nmp[x][Z];
		tX.C += mul;
		if(!tX.C) {
			nmp[x].erase(Z);
		} else {
			tX.A += mul * dist(u, x);
			tX.B += mul * dist(u, par[x]);
		}
		if(x == par[x]) break;
	}
}

void upd(int u, bool add) {
	if(add) {
		updTree(u, add);
		updAns(u, add);
	} else {
		updAns(u, add);
		updTree(u, add);
	} 
}

//=========================================MAIN============================================

int main(){
	
	int m, q, ac;
	scanf("%d %d %d %d", &n, &m, &q, &ac);

	for(int i = 1; i <= n; ++i) {
		scanf("%d", &V[i]);
	}
	
	for(int i = 2; i <= n; ++i) {
		int v;
		scanf("%d", &v);
		e[v].pb(i);
		e[i].pb(v);
	}

	for(int i = 1; i <= m; ++i) {
		scanf("%d", &CS[i]);
	}

	L[1] = 1;
	getLevel(1);
	prepAncestor();
	decompose(1);
	
	for(int i = 1; i <= n; ++i) {
		upd(i, true);
	}

	while(q--) {
		int t;
		scanf("%d", &t);
		if(t == 1) {
			int u, v;
			scanf("%d %d", &u, &v);
			upd(u, false);
			V[u] = v; 
			upd(u, true);
		}
		else if(t == 2) {
			int v;
			scanf("%d", &v);
			long double ans = S[v] * T[v] - D[v] / 2;

			ans *= 1LL * CS[v] * CS[v];


			ans += 1LL * n * ac * ac;

			
			long long anst = 2LL * CS[v] * ac * S[v];
			
			ans -= anst;

			cout << fixed << setprecision(12) << ans / n << "\n"; 
		}
	}
}