Divisors of a Binomial Coefficient

Time limit1sMemory limit256 MB

Summary

For each pair n and k, count the distinct divisors of the binomial coefficient C(n, k), where n is at most 431.

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

Problem

Given two integers $n$ and $k$ , determine the number of distinct divisors of the binomial coefficient $\binom{n}{k}$ .

Input

The input consists of several test cases. Each test case is a single line containing two integers $n$ and $k$ ( $0 \le k \le n \le 431$ ), separated by a single space. Input continues until end of file (EOF).

Output

For each test case, output a single line containing one integer — the number of distinct divisors of $\binom{n}{k}$ . For the given inputs, this value does not exceed $2^{63}-1$ .

Examples1

Example 1
Input
```
5 1
6 3
10 4
```
Expected output
```
2
6
16
```