Problems
Save Walle
Save Walle
Robot Walle is located in the coordinate plane at (0, 0). Calculate the number of ways in which the Walle can get to the position (ex, ey) provided that the position (x, y) can be reached only from the point (x - 1, y) or (x, y - 1), and must hold the conditions x \ge y and x \cdot y is even.
Input data
Two positive integers ex, ey~(1 \le ex, ey \le 100).
Output data
Print the number of ways modulo 10^9 + 7.
Examples
Input example #1
2 2
Output example #1
1
Input example #2
6 2
Output example #2
3
Input example #3
8 8
Output example #3
14