4141

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

SAMPLE INPUT
5
1 4 6 2
4 1 4 2
8 2 1 2
2 8 8 2
1 2 1 3

SAMPLE OUTPUT
NO
YES
YES
NO
YES

Explanation

Numbers: 14, 41, 82, 28, 123.

Source: hackerearth | Difficulty: EASY
Tags: Number theory

Mathematics


Solutions: