OnlineJudge 3 现已推出。点此体验新版：HEX | SDUT OnlineJudge

### HEX

Time Limit: 4000 ms
Memory Limit: 131072 KiB

#### Problem Description

On a plain of hexagonal grid, we define a step as one move from the current grid to the lower/lower-left/lower-right grid. For example, we can move from (1,1) to (2,1), (2,2) or (3,2).

In the following graph we give a demonstrate of how this coordinate system works.

Your task is to calculate how many possible ways can you get to grid(A,B) from gird(1,1), where A and B represent the grid is on the B-th position of the A-th line.

#### Input

For each test case, two integers A (1<=A<=100000) and B (1<=B<=A) are given in a line, process till the end of file, the number of test cases is around 1200.

#### Output

For each case output one integer in a line, the number of ways to get to the destination MOD 1000000007.

#### Sample Input

1 1 3 2 100000 100000

#### Sample Output

1 3 1

#### Hint

#### Source

“浪潮杯”山东省第八届ACM大学生程序设计竞赛（感谢青岛科技大学）