B'You are given a binary string s of length n (a string consisting of n characters, and each character is either 0 or 1). Let 's look at s as at a binary representation of some integer, and name that integer as the value of string s . For example, the value of 000 is 0 , the value of 01101 is 13 , "100000" is 32 and so on. You can perform at most k operations on s . Each operation should have one of the two following types: What is the minimum value of s you can achieve by performing at most k operations on s ? The first line contains two integers n and k ( 2 <= n <= 5 cdot 10^5 ; 1 <= k <= n ) -- the length of the string s and the maximum number of operations. The second line contains the string s of length n consisting of characters 0 and/or 1. Additional constraint on the input: s contains at least one 1. Print a single integer -- the minimum value of s you can achieve using no more than k operations. Since the answer may be too large, print it modulo 10^{9} + 7 . Note that you need to minimize the original value, not the remainder. In the first example, one of the optimal strategies is the following: In the second example, one of the optimal strategies is the following: '...