140. Integer Sequences

time limit per test: 0.25 sec.
memory limit per test: 4096 KB

A sequence A is called an integer sequence of length N if all its elements A₁ A₂ .. A_N are non-negative integers less than 2 000 000 000. Consider two integer sequences of length N, A and X. The result of their multiplication (A*X) is an integer number R=A₁*X₁ + A₂*X₂ + .. + A_N*X_N. Your task is to solve the equation A*X=B (mod P), given the integer sequence A and the integer numbers B and P.

Input

The first line contains the integer numbers N (1<=N<=100) - the length of the integer sequences - P (1<=P<=10 000) and B (0<=B<=P-1). The second line contains the elements of the sequence A, separated by blanks: A₁ A₂ .. A_N.

Output

You should print one line containing the word "YES" if there exists at least one integer sequence X which is a solution to the equation, or print "NO" otherwise. If the answer is "YES", the next line should contain N non-negative integers separated by blanks: X₁ X₂ .. X_N.

Sample Input #1

2 7 4
7 3

Sample Output #1

YES
0 6

Sample Input #2

3 10 1
2 4 6

Sample Output #2

NO