You sleep while we work: due to technical reasons Codeforces may be unavailable on May 22 on time interval 01:00-03:00 (MSK). ×

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 .. AN 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 + .. + AN*XN. 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 .. AN.

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 .. XN.

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


 Author : Mugurel Ionut Andreica Resource : SSU::Online Contester Fall Contest #2 Date : Fall 2002