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Given a positive integers $n$ , Mobius function $\mu(n)$ is defined as follows:

$$\displaystyle \mu(n) = \begin{cases} 1 &n = 1 \\ (-1)^k & n = p_1p_2\cdots p_k \\ 0 &other \end{cases}$$

$p_i (i = 1, 2, \cdots, k)$ are different prime numbers.

Given two integers $m$, $n$, please calculate $\sum_{i = 1}^{m} \mu(in)$.

Input

One line includes two integers $m (1 \le m \le 2e9)$, $n (1 \le n \le 1e12)$ .

Output

One line includes the answer .

样例输入

2 2

样例输出

-1

• main.c