BLUE is learning binary numbers. There is an easy problem in his homework.

You are given a binary number s_1∼n (s₁ is the highest bit. s_n is the lowest bit.). You need to do an operation exactly k times: select an interval [l, r] (1 ≤ l ≤ r ≤ n) arbitrarily and flip s_l , s_l+1, ..., s_r, in other word, for all i ∈ [l, r], s_i becomes 1 if s_i is 0, s_i becomes 0 if s_i is 1. What is the biggest result binary number after the k operations.

BLUE found useless algorithms useless on the problem, so he asked ACMZYX to help. ACMZYX looked down on the problem but finally got WA (wrong answer). Can you help them to find the correct solution?

The first line of the input contains a single integer T (1 ≤ T ≤ 6 × 10⁴ ), indicating the number of test cases
In each test case: 
The first line contains two integers n, k. (1 ≤ n ≤ 10⁵ , 0 ≤ k ≤ 10¹⁸) 
The second line contains a binary number s_1∼n. (s₁ = 1, ∀i ∈ [2, n] : s_i ∈ {0, 1}) 
It’s guarenteed that in all test cases, ∑n ≤ 2.5 × 10⁶

You need to print a string of length n in one line, representing the biggest binary number after the k operations.

 2023“钉耙编程”中国大学生算法设计超级联赛（2）