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 A_{1} A_{2} .. 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=A_{1}*X_{1} + A_{2}*X_{2} + .. + 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: A_{1} A_{2} .. 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: X_{1} X_{2} .. X_{N}.