Power Board

题意翻译

有一个 $n\times m$ 的矩阵，第 $i$ 行第 $j$ 列上写着 $i^j$。 问矩阵中有多少个不同的数。 $1\le n,m\le 10^6$。

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.

输入输出格式

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

输入样例 #1

3 3

输出样例 #1

7

输入样例 #2

2 4

输出样例 #2

5

输入样例 #3

4 2

输出样例 #3

6

说明

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 $ .