2018.04.05 update: 今天无意间重新翻开了博客发现了这个历史遗留问题，已经知道是卡特兰数了，但由于取模的数不是素数啊。。。好像还是不太会做。
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不会做。打表打不起来，只知道规律。
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
| 1 | 1 | |||||||
| 2 | 2 | 2 | ||||||
| 3 | 3 | 5 | 5 | |||||
| 4 | 4 | 9 | 14 | 14 | ||||
| 5 | 5 | 14 | 28 | 42 | 42 | |||
| 6 | 6 | 20 | 48 | 90 | 132 | 132 | ||
| 7 | 7 | 27 | 75 | 165 | 297 | 429 | 429 |
规律：
a[i][1]=i;
a[i][i]=a[i][i-1];
a[i][j]=a[i-1][j]+a[i][j-1];
Problem Description
Recently, lxhgww received a task : to generate strings contain '0's and '1's only, in which '0' appears exactly m times, '1' appears exactly n times. Also, any prefix string of it must satisfy the situation that the number of 1's can not be smaller than the number of 0's . But he can't calculate the number of satisfied strings. Can you help him?
Input
T(T<=100) in the first line is the case number.
Each case contains two numbers n and m( 1 <= m <= n <= 1000000 ).
Each case contains two numbers n and m( 1 <= m <= n <= 1000000 ).
Output
Output the number of satisfied strings % 20100501.
Sample Input
1
2 2
Sample Output
2