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Power Board

1000ms 262144K

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.

Sample Input:

3 3

Sample Output:

7

Sample Input:

2 4

Sample Output:

5

Sample Input:

4 2

Sample Output:

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 $$$16$$$.

Informação

Codeforces

Provedor Codeforces

Código CF1646E

Tags

brute forcedpmathnumber theory

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Datas 09/05/2023 10:22:45

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