Furik loves math lessons very much, so he doesn't attend them, unlike Rubik. But now Furik wants to get a good mark for math. For that Ms. Ivanova, his math teacher, gave him a new task. Furik solved the task immediately. Can you?

You are given a system of equations:

You should count, how many there are pairs of integers $(*a*, *b*)$ $(0 ≤ *a*, *b*)$ which satisfy the system.

Input

A single line contains two integers $*n*, *m*$ $(1 ≤ *n*, *m* ≤ 1000)$ — the parameters of the system. The numbers on the line are separated by a space.

Output

On a single line print the answer to the problem.

Note

In the first sample the suitable pair is integers $(3, 0)$. In the second sample the suitable pair is integers $(3, 5)$. In the third sample there is no suitable pair.