Fibonacci series is a series in which every element is sum of previous 2 elements.

The first 2 elements are 0, 1 and the series goes like 0, 1, 1, 2, 3, 5, 8, 13...

What if you were given 2 random numbers as the starting of the series and you follow the same rule as the Fibonacci rule?

For example, if you were given 2 and 2 .. the series would become:

2 2 4 6 10 16 26...

Now your task is simple...

You will be given 2 numbers a and b - the first and second term of the series.

You need to calculate the sum of first n numbers of the series so formed.

Since the numbers can be big you need to print the result mod some number 'M' provided in the input.

Input

The first line will have single number 't' - number of test cases.

Each test case will have 4 numbers a, b, n and M.

a - first number of the series.

b - second number of the series.

n - calculate the sum for n terms.

M - give the result mod M.

Output

single number for each case - sum of n terms mod M.

Example

Input:
2
2 2 10 21
1 3 10 21

Output:
13
4

Explanation

The first case series is 2 2 4 6 10 16 26 42 68 110, sum is 286, result is 286 % 21 = 13.

Constraints

Number of test cases ≤ 100.
0 ≤ a, b, m ≤ 10⁸.
1 ≤ n ≤ 10⁸.