Mohamed Yasser (AKA Abo-3obaida) and Mohamed Ahmed (AKA Nesr) pretend to be rivals, the two clearly have a deep and understanding friendship.

One day they imagine that the city is a 2D plane with Cartesian coordinate system, the two rivals are located in point (0, 0), and they are targeting point (X, Y).

They can make two moves only:

1. move right to the point (X + 1, Y).
2. move up to the point (X, Y + 1).

Nesr immediately said: "I've figured out how many ways are there to reach our target".
Abo-3obaida replied: "I'll not lose this challenge".

Could you help Abo-3obaida to figure out how many ways to the target?!

Since the required number may be very large, find its remainder of division by 1000000007 (10⁹ + 7).

Input

The first line of input contains an integer T (1 <= T <= 1000) followed by T test cases.

Each case contains two space-separated integers  X,  Y (0 <= X, Y <= 10⁶).

Output

For each test case, print a single integer the answer to the problem modulo 1000000007 (10⁹ + 7).

Example

Input:
3
1 3
2 4
5 3

Output:
4
15
56