CF1646E.Power Board

普及/提高-

通过率：0%

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题目描述

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.

输入格式

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.

输出格式

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

输入输出样例

输入#1
```
3 3
```
输出#1
```
7
```
输入#2
```
2 4
```
输出#2
```
5
```
输入#3
```
4 2
```
输出#3
```
6
```

说明/提示

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 $16$ .

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