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- Practice
- Mathematics
- Number Theory
- Closest Number

# Closest Number

# Closest Number

You are given 3 numbers *a*, *b* and *x*. You need to output the multiple of *x* which is closest to *a ^{b}*. If more than one answer exists , display the smallest one.

**Input Format**

The first line contains *T*, the number of testcases.

*T* lines follow, each line contains 3 space separated integers (*a*, *b* and *x* respectively)

**Constraints**

1 ≤ *T* ≤ 10^{5}

1 ≤ *x* ≤ 10^{9}

0 < *a ^{b}* ≤ 10

^{9}

1 ≤

*a*≤ 10

^{9}

-10

^{9}≤

*b*≤ 10

^{9}

**Output Format**

For each test case , output the multiple of *x* which is closest to *a ^{b}*

**Sample Input 0**

```
3
349 1 4
395 1 7
4 -2 2
```

**Sample Output 0**

```
348
392
0
```

**Explanation 0**

The closest multiple of 4 to 349 is 348.

The closest multiple of 7 to 395 is 392.

The closest multiple of 2 to 1/16 is 0.