Find 7 Faster Than John Von Neumann

Time Limit: Java: 1000 ms / Others: 1000 ms

Memory Limit: Java: 32768 KB / Others: 32768 KB

Description

It was said that when testing the first computer designed by von Neumann, people gave the following problem to both the legendary professor and the new computer: If the 4th digit of 2^n is 7, what is the smallest n? The machine and von Neumann began computing at the same moment, and von Neumann gave the answer first.

Now you are challenged with a similar but more complicated problem: If the K-th digit of M^n is 7, what is the smallest n?

Input

Each case is given in a line with 2 numbers: K and M (< 1,000).

Output

For each test case, please output in a line the smallest n.

You can assume:

  • The answer always exist.
  • The answer is no more than 100.
  • Sample Input

    3 2
    4 2
    4 3

    Sample Output

    15
    21
    11

    Hint

    None

    Source

    ZOJ 7th Anniversary Contest

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