Cifera · Interview Problem

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Codeforces

Easy

Math

Number Theory

Cifera

Determine whether one number is a power multiple of another by repeatedly multiplying and checking divisibility.

Acceptance 0%

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Problem Statement

Problem

You are given two positive integers $a$ and $b$ . Determine whether there exists a non-negative integer $k$ such that

$b = a^k$

If such a $k$ exists, the numbers are related; otherwise, they are not.

In practice, this means you should verify whether $b$ can be obtained by starting from $a$ and repeatedly multiplying by $a$ until reaching $b$ exactly.

Input Format

The first line contains two integers $a$ and $b$ .

Output Format

Print YES if $b$ is a power of $a$ .
Otherwise, print NO.

Constraints

$1 \le a, b \le 10^9$

Hints

Repeatedly divide $b$ by $a$ while it is divisible.
If the process ends at $1 $, then$ b $was a power of$ a$.

Input Format

One line with two integers $a$ and $b$ .

Output Format

Output YES if $b$ is a power of $a, otherwise output NO`.

Constraints

$1 \le a, b \le 10^9$

Examples

Sample cases returned by the problem API.

Example 1

Input

2 8

Output

YES

Explanation

Since $8 = 2^3$ , the answer is YES.

Example 2

Input

3 10

Output

NO

Explanation

No integer power of $3 $equals \$ 10`.

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