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## Problem Statement

Rar the Cat is tired of cooking up stories to make a problem look interesting. Since this is a math problem, it wouldn't be interesting anyway.

While doing `exponentiate`

, Rar always wondered how many digits *A ^{B}* is, for the value of

*A*and

*B*which Rar the Cat will provide.

Both *A* and *B* will be strictly positive and will fit into a 64-bit signed integer (long long).

## Input

There are multiple testcases for this problem, the first line of input will indicate the number of testcases, *TC*.

*TC* lines follow and each line will have *A* and *B*

## Output

For each testcase, output the number of digits of *A ^{B}*

## Subtasks

Subtask 1 (13%): *TC* = 1, it is also guaranteed that *A ^{B}* ≤ 2,000,000,000

Subtask 2 (28%): *TC* = 1, no other restrictions

Subtask 3 (59%): 0 ≤ *TC* ≤ 1000000

## Sample Input 1

5 2 1 2 2 2 3 2 4 2 5

## Sample Output 1

1 1 1 2 2

## Explanation for Sample Output 1

The input is asking for the number of digits for the powers of 2. The first 5 powers of 2 are : 2, 4, 8, 16, 32 and thus they are of 1, 1, 1, 2, 2 digits respectively.

## Sample Input 2

1 123456789 123456789

## Sample Output 2

998952458

### Tags

### Subtasks and Limits

Subtask | Score | #TC | Time | Memory | Scoring |
---|---|---|---|---|---|

1 | 13 | 50 | 2s | 32MB | Minimum |

2 | 28 | 60 | 2s | 32MB | Minimum |

3 | 59 | 30 | 2s | 32MB | Minimum |

4 | 0 | 2 | 2s | 32MB | Minimum |

### Judge Compile Command

g++-8 ans.cpp -o digits -Wall -Wshadow -static -O2 -lm -m64 -s -w -std=gnu++17 -fmax-errors=512