I was going through this question which uses DP + Bitmask. But the editorial is too brief to understand and the author assumes everyone's familiarity with DP + Bitmask.

In my understanding,

    for (int i = 1 ; i <= n ; i ++) {
    	for (int k = 1 ; k < 60 ; k ++) {
    		int x = (~fact[k]) & ((1 << 17) - 1);
    		for (int s = x ; ; s = (s - 1) & x) {
                if (dp[i - 1][s] + abs(a[i] - k) < dp[i][s | fact[k]]){
                    dp[i][s | fact[k]] = dp[i-1][s] + abs(a[i]-k);
                }
    		if (s == 0) break;
            }
    	}
    }

We iterate through all the possible values of k , ORing it every time which includes the prime factors in the answer. But why do we add abs(a[i] - k) in the dp, how does it help in identifying the answer? And once the dp matrix is set how do we retrieve the answer? Any help on the problem is appreciated.