Solve the programming task below in a Python markdown code block.
Read problems statements in Mandarin chinese, Russian and Vietnamese as well. 

Chef is tired of solving boring math problems by hand. One of these problems is summing up the products of elements from each k-subset of the set [n]. Here, a k-subset is a subset containing exactly k elements and [n] refers to the set which contains all integers between 1 and n (inclusive). More formally:

Let’s denote this number by f(n, k). Note that f(n, 0) = 1.

Since calculating f(n, k) is too boring, Chef wants to know how the divisibility of f(n, k) by a given prime p depends on k. Specifically, for a fixed n, you should compute the number of ways to select k (0 ≤ k ≤ n) so that f(n, k) isn't divisible by p. After a while of thinking, Chef realized there might be too many ways to do that. Therefore, you should compute this number modulo 10^{9}+7.

------ Input ------ 

The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
The first and only line of each test case contains two space-separated integers n and p.

------ Output ------ 

For each test case, print a single line containing one number — the number of ways to select k, modulo 10^{9}+7.

------ Constraints ------ 

$1 ≤ T ≤ 4$
$1 ≤ n < 10^{501}$
$n does not contain leading zeroes$
$2 ≤ p ≤ 100,000$
$p is prime$

------ Subtasks ------ 

Subtask #1 (10 points): n ≤ 5,000

Subtask #2 (40 points): n ≤ 100,000

Subtask #3 (50 points): original constraints

----- Sample Input 1 ------ 
1
4 2
----- Sample Output 1 ------ 
2
----- explanation 1 ------ 
Example case 1: The values of f(4, k) are as follows:

f(4, 0) = 1
f(4, 1) = 1+2+3+4 = 10
f(4, 2) = 1·2+2·3+3·4+4·1+1·3+2·4 = 35
f(4, 3) = 1·2·3+2·3·4+1·3·4+1·2·4 = 50
f(4, 4) = 1·2·3·4 = 24

Only k = 0 and k = 2 give numbers indivisible by p = 2, so the answer is 2.