BPC 1 J4 - Assignment of the Year

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Points: 10 (partial)
Time limit: 1.5s
Memory limit: 512M

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Problem type

This year at Spirit of Math Schools, you have been assigned to find the number of unique numbers between 0 and M (inclusive) you can create using a list of N digits. You may add or concatenate digits. Their order must be maintained, and every digit must be used. Output the number of unique values you can create between 0 and M.

Constraints

1 \le N \le M \le 10^4

Subtask 1 [10%]

All of the digits are the same.

Subtask 2 [90%]

No additional constraints.

Input Specification

The first line contains two integers, N and M.

The next line contains a string of N digits (numbers between 0 and 9).

Output Specification

Output a single line containing an integer, the number of unique values that can be created.

Sample Input

4 100
1996

Sample Output

2

Explanation for Sample

There are 8 possible combinations of operations:

\displaystyle \begin{align*}
1+9+9+6 &= 25 \\1+9+96 &= 106 \\1+99+6 &= 106 \\1+996 &= 997 \\19+9+6 &= 34 \\19+96 &= 115 \\199+6 &= 205 \\1996 &= 1996
\end{align*}

Only two of these are between 0 and 100 (25 and 34).


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