Farmer Jane needs to be able to measure out corn to feed her cows, but all she has to help her is a primitive balance scale and a $6$ kilogram rock. With this rock she could use the balance scale to measure out $6$ kg of corn, but she often needs to measure out smaller quantities. She figures out that if she breaks the rock into three pieces, where two of them are $1$ kg and the third is $4$ kg, then she can measure out all integer quantities of corn from $1$ to $6$, as shown below.

Farmer Jane is happy now, but the situation gets her thinking. She knows she could have broken the rock into $1$, $2$, and $3$ kg pieces and this would also have worked. But things are not so simple for other numbers. For example, there are $15$ ways to break a $12$ kg rock into $4$ integer pieces but only $9$ of them let you measure all integer weights from $1$ to $12$. She wonders if there could be some kind of algorithm to determine how many combinations work for a given size of rock and a given number of pieces…

The input contains $10$ test cases.

Each test case consists of two integers ($P$ and $R$) on a single line separated by a space. The integer $P$ gives the number of pieces to break the rock into and the integer $R$ gives the original size of the rock. For all test cases, $1\le R\le 100$.

For the first $5$ test cases $3\le P\le 5$ and for the next $5$ test cases $6\le P\le 10$.

Your job is to output a single line for each test case indicating the number of ways you can break up the rock into $P$ integer-sized pieces so that all possible integer weights from $1$ to $R$ can be measured on a balance scale.

Sample Input

3 6
4 12
4 30
5 40
5 5
6 25
7 55
8 65
9 75
10 85

Sample Output

2
9
5
137
1
154
5749
28051
121108
474402

Educational Computing Organization of Ontario - statements, test data and other materials can be found at ecoocs.org