Link to Russian translation of problem

The statement of this problem is very simple: you are given a non-negative integer X. Whether it's divisible by 41?

Input
The first line contains one integer T - denoting the number of test cases. The following T lines contain 4 integers a[0], a1, c, n each and describe each test case:

Let's consider decimal representation of the number X as an array where a[0] is the leftmost (highest) digit. You are given a[0], a1 and each a[i] for 2 <= i <= n-1 can be found by formula:

a[i] = ( a[i - 1]*c + a[i - 2] ) modulo 10

Output
For each test case output YES if the corresponding integer is divisible by 41 and NO otherwise.

Constraints

• T <= 2000
• 1 <=N <= 50000
• 0 <= a[0], a1, c < 10