A8345. Lucky Transformation

Petya 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.

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.

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

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

In the second sample: $4478→4778→4478$ .