Editorial

The required path is a broken line consisting of $n+m$ links. Of these, $n$ links must be vertical, and the rest must be horizontal. The number of ways to choose $n$ vertical links out of $n+m$ is equal to $C_{n+m}^n$.

Example

For the first test case $n=3,m=4$. The answer is $C_7^3=\frac{7!}{3!\cdot 4!}=\frac{7\cdot 6\cdot 5}{1\cdot 2\cdot 3}=35$.

For the second test case $n=1,m=1$. The answer is $C_2^1=\frac{2!}{1!\cdot 1!}=2$.

Algorithm realization

The function Cnk computes the value of the binomial coefficient $C_n^k$.

long long Cnk(long long n, long long k)
{
  long long res = 1;
  if (k > n - k) k = n - k;
  for (long long i = 1; i <= k; i++)
    res = res * (n - i + 1) / i;
  return res;
}

The main part of the program. Read the input data.

scanf("%lld %lld", &n, &m);

Compute and print the answer $C_{n+m}^n$.

res = Cnk(n + m, n);
printf("%lld\n", res);

Python realization

import math

Read the input data.

n, m = map(int,input().split())

Compute and print the answer $C_{n+m}^n$.

res = math.comb(n + m, n)
print(res)