Counting Perfect Square Products

Given two positive integers n and m, calculate the sum

$$\sum_{i=1}^{n}{\sum_{j=1}^{m}\left|f(i \times j)\right|}$$

where \(|f(x)|\) is defined as follows:

• If x is a perfect square then \(|f(x)| = 1\).
• Otherwise, \(|f(x)| = 0\).

A perfect square is an integer that can be expressed as the square of another integer. In other words, an integer \(x\) is a perfect square if there exists an integer \(k\) such that \(x=k^2\).

Your task is to output the computed sum.

inputFormat

The input consists of a single line containing two space-separated positive integers, n and m.

outputFormat

Output a single integer which is the value of the sum \(\sum_{i=1}^{n}{\sum_{j=1}^{m}\left|f(i \times j)\right|}\).

sample

1 1

1