Aniahasalargeinteger SS.Itsdecimalrepresentationhaslength nn anddoesn'tcontainanyleadi
Ania has a large integer S">SS. Its decimal representation has length n">nn and doesn‘t contain any leading zeroes. Ania is allowed to change at most k">kk digits of S">SS. She wants to do it in such a way that S">SS still won‘t contain any leading zeroes and it‘ll be minimal possible. What integer will Ania finish with?
Input
The first line contains two integers n">nn and k">kk (1&＃x2264;n&＃x2264;200000">1≤n≤2000001≤n≤200000, 0&＃x2264;k&＃x2264;n">0≤k≤n0≤k≤n) — the number of digits in the decimal representation of S">SSand the maximum allowed number of changed digits.
The second line contains the integer S">SS. It‘s guaranteed that S">SS has exactly n">nn digits and doesn‘t contain any leading zeroes.
Output
Output the minimal possible value of S">SS which Ania can end with. Note that the resulting integer should also have n">nn digits.
Examples
input
Copy
5 3
51528
output
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10028
input
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3 2
102
output
Copy
100
input
Copy
1 1
1
output
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0
Note
A number has leading zeroes if it consists of at least two digits and its first digit is 0">00. For example, numbers 00">0000, 00069">0006900069 and 0101">01010101 have leading zeroes, while 0">00, 3000">30003000 and 1010">10101010 don‘t have leading zeroes.
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