#P1646E. Power Board

Power Board

Description

You have a rectangular board of size n×mn\times m (nn rows, mm columns). The nn rows are numbered from 11 to nn from top to bottom, and the mm columns are numbered from 11 to mm from left to right.

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

Find the number of distinct integers written on the board.

The only line contains two integers nn and mm (1n,m1061\le n,m\le 10^6) — the number of rows and columns of the board.

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

Input

The only line contains two integers nn and mm (1n,m1061\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

样例输入 1

3 3

样例输出 1

7

样例输入 2

2 4

样例输出 2

5

样例输入 3

4 2

样例输出 3

6

Note

The statement shows the board for the first test case. In this case there are 77 distinct integers: 11, 22, 33, 44, 88, 99, and 2727.

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

There are 55 distinct numbers: 11, 22, 44, 88 and 1616.

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

There are 66 distinct numbers: 11, 22, 33, 44, 99 and 1616.