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Tracy is teaching Charlie maths via a game called $N$-Cube, which involves three sections involving $N$.

Tracy gives Charlie a number $N$, and Charlie makes a list of $N$-th powers of integers in increasing order $1^N, 2^N, 3^N, \dot, \text{so on}$. This teaches him exponentiation.

Then Charlie performs the following subtraction game $N$ times: Take all pairs of consecutive numbers in the list and take their difference. These differences then form the new list for the next iteration of the game. Eg, if $N$ was 6, the list proceeds as $[1, 64, 729, 4096 ... ]$ to $[63, 685, 3367 ...]$, and so on $5$ more times.

After the subtraction game, Charlie has to correctly tell Tracy the $N$-th element of the list. This number is the *value of the game*.

After practice Charlie became an expert in the game. To challenge him more, Tracy will give two numbers $M$ (where $M$ is a prime) and $R$ instead of just a single number $N$, and the game must start from $M_R - 1$ instead of $N$. Since the *value of the game* can now become large, Charlie just have to tell the largest integer $K$ such that $M_K$ divides this number. Since even $K$ can be large, output $K$ modulo 1000000007 ($10^9 + 7$).

###Input:

- First line will contain $T$, number of testcases. Then the testcases follow.
- Each testcase contains of a single line of input, two integers $M, R$.

###Output:
For each testcase, output in a single line answer given by Charlie to Tracy modulo 1000000007.

###Constraints
- $1 \leq T \leq 1000$
- $2 \leq M \leq 10^9$

###Subtasks
- 30 points : $1 \leq R \leq 10000$
- 70 points : $1 \leq R \leq 10^9$

$M$ is a prime number

###Sample Input:
	1
	2 2

###Sample Output:
	1

###EXPLANATION:
This list is :
$[1,8,27,64,125..] -> [7,19,37,61..] -> [12,18,24..] -> [6,6,6..]$. Number of times 2 divides 6 is 1. Hence the answer is 1.