Description

You have a rectangular board of size $n\times m$ ($n$ rows, $m$ columns). The $n$ rows are numbered from $1$ to $n$ from top to bottom, and the $m$ columns are numbered from $1$ to $m$ from left to right.

The cell at the intersection of row $i$ and column $j$ contains the number $i^j$ ($i$ raised to the power of $j$). For example, if $n=3$ and $m=3$ the board is as follows:

Find the number of distinct integers written on the board.

Input

The only line contains two integers $n$ and $m$ ($1\le n,m\le 10^6$) — the number of rows and columns of the board.

Output

Print one integer, the number of distinct integers on the board.

Samples

3 3

7

2 4

5

4 2

6

Note

The statement shows the board for the first test case. In this case there are $7$ distinct integers: $1$, $2$, $3$, $4$, $8$, $9$, and $27$.

In the second test case, the board is as follows:

There are $5$ distinct numbers: $1$, $2$, $4$, $8$ and $16$.

In the third test case, the board is as follows:

There are $6$ distinct numbers: $1$, $2$, $3$, $4$, $9$ and $16$.