Average

Time limit1sMemory limit512 MB

Summary

Count, over all N-tuples of integer marks from 0 to fullmarks, the total number of teachers whose mark equals the tuple's mean, modulo 1000000007.

Level: Medium7 of 10
Topics: Combinatorics, Dynamic programming, Math
Solved: No attempts yet

Problem

$N$ teachers grade one student's presentation. Each teacher gives one integer from 0 to fullmarks, inclusive. The student's final score is the arithmetic mean of these $N$ marks.

Every mark is an integer, but the mean can still be a fraction. Sometimes the mean is an integer, and in some of those cases a teacher's mark equals the mean exactly. One teacher whose mark equals the mean is called a matching event.

Consider every combination of marks the teachers can give. If $k$ teachers gave a mark equal to the mean in one combination, that combination produces $k$ matching events. Count the total number of matching events over all combinations.

Input

The input holds several test cases, at most 1001 of them.

Each test case is one line with two integers $N$ and fullmarks, where $2 \le N \le 60$ and $1 \le \text{fullmarks} \le 200$ . $N$ is the number of teachers grading the student, and fullmarks is the largest mark a teacher can give. The smallest mark a teacher can give is always 0.

A line holding two zeros ends the input. Do not process that line.

Output

For each test case, print one line holding $M$ modulo $1000000007$ , where $M$ is the total number of matching events.

Examples3

Example 1
Input
```
4 100
3 1
0 0
```
Expected output
```
1373732
6
```
Example 2
Input
```
2 1
0 0
```
Expected output
```
4
```
Example 3
Input
```
3 200
5 7
2 3
0 0
```
Expected output
```
60603
5120
8
```