SSR

Time limit2sMemory limit512 MB

Summary

Count ordered pairs (A, B) with A <= N and B <= M for which (sqrt(A) + sqrt(B))^2 is an integer.

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

Problem

For two positive integers $A$ and $B$ , define $\mathrm{SSR}(A, B) = (\sqrt{A} + \sqrt{B})^2$ .

Given two integers $N$ and $M$ , write a program that counts the ordered pairs $(A, B)$ with $1 \le A \le N$ and $1 \le B \le M$ for which $\mathrm{SSR}(A, B)$ is an integer.

Input

The first line contains $N$ and $M$ , separated by a space. ( $1 \le N, M \le 77777$ )

Output

Print the number of ordered pairs $(A, B)$ that satisfy the condition on the first line.

Examples3

Example 1
Input
```
2 2
```
Expected output
```
2
```
Example 2
Input
```
10 1
```
Expected output
```
3
```
Example 3
Input
```
3 8
```
Expected output
```
5
```