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B. Lucky Transformation

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPetya loves lucky numbers. Everybody knows that lucky numbers are positive integers whose decimal representation contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.

Petya has a number consisting of *n* digits without leading zeroes. He represented it as an array of digits without leading zeroes. Let's call it *d*. The numeration starts with 1, starting from the most significant digit. Petya wants to perform the following operation *k* times: find the minimum *x* (1 ≤ *x* < *n*) such that *d*_{x} = 4 and *d*_{x + 1} = 7, if *x* is odd, then to assign *d*_{x} = *d*_{x + 1} = 4, otherwise to assign *d*_{x} = *d*_{x + 1} = 7. Note that if no *x* was found, then the operation counts as completed and the array doesn't change at all.

You are given the initial number as an array of digits and the number *k*. Help Petya find the result of completing *k* operations.

Input

The first line contains two integers *n* and *k* (1 ≤ *n* ≤ 10^{5}, 0 ≤ *k* ≤ 10^{9}) — the number of digits in the number and the number of completed operations. The second line contains *n* digits without spaces representing the array of digits *d*, starting with *d*_{1}. It is guaranteed that the first digit of the number does not equal zero.

Output

In the single line print the result without spaces — the number after the *k* operations are fulfilled.

Examples

Input

7 4

4727447

Output

4427477

Input

4 2

4478

Output

4478

Note

In the first sample the number changes in the following sequence: 4727447 → 4427447 → 4427477 → 4427447 → 4427477.

In the second sample: 4478 → 4778 → 4478.

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