hdu 3398 String

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 ).

 

 

Output

 

Output the number of satisfied strings % 20100501.

 

Sample Input

 

1 2 2

Sample Output

 

2