Problem
Illuso has a large number of S.
The decimal representation of this number consists of n digits and does not contain leading zeros.
Illuso can change at most k digits in S. He wants to do this so that S still has no leading zeros and is as small as possible.
What number will Illuso end up with?
Input
The first line contains two integers n and k (1 ≤ n ≤ 200000, 0 ≤ k ≤ n) — the number of digits in decimal notation S and the maximum number of digits that can be modified.
The second line contains an integer S. It is guaranteed that S consists of exactly n digits and does not contain any leading zeros.
Imprint
Print the minimum possible number S that Illuso can get.
Note that the resulting number must have exactly n digits.
Examples
| Input |
Output |
5 3
51528 |
10028 |
3 2
102 |
100 |
1 1
1 |
0 |