The Monkey King

As everyone known, The Monkey King is Son Goku. He and his offspring live in Mountain of Flowers and Fruits. One day, his sons get $n$ peaches. And there are $m$ monkeys (including GoKu), they are numbered from $1$ to $m$, GoKu’s number is 1. GoKu wants to distribute these peaches to themselves. Since GoKu is the King, so he must get the most peach. GoKu wants to know how many different ways he can distribute these peaches. For example n=2, m=3, there is only one way to distribute these peach: 2 0 0.

When given $n$ and $m$, you are expected to calculate how many different ways GoKu can distribute these peaches. Answer may be very large, output the answer modular $1000000007$ instead.

There are multiple test cases. In the first line of the input file there is an integer $T$ indicates the number of test cases.

In the next $T$ lines, each line contains $n$ and $m$ which is mentioned above.

[Technical Specification]

All input items are integers.

$1 \leq T \leq 25$

$1 \leq n,m \leq 100000$

For each case，the output should occupies exactly one line.

See the sample for more details.

2
2 2
3 5

1
5

For the second case, there are five ways. They are
2 1 0 0 0
2 0 1 0 0
2 0 0 1 0
2 0 0 0 1
3 0 0 0 0

BestCoder Round #36 ($)