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~).