You are given an integer x of n digits a1,a2,…,an, which make up its decimal notation in order from left to right.
Also, you are given a positive integer k<n.
Let's call integer b1,b2,…,bm beautiful if bi=bi+k for each i, such that 1≤i≤m−k.
You need to find the smallest beautiful integer y, such that y≥x.
The first line of input contains two integers n,k (2≤n≤200000,1≤k<n): the number of digits in x and k.
The next line of input contains n digits a1,a2,…,an (a1≠0, 0≤ai≤9): digits of x.
In the first line print one integer m: the number of digits in y.
In the next line print m digits b1,b2,…,bm (b1≠0, 0≤bi≤9): digits of y.
3 2 353
3 353
4 2 1234
4 1313