13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T6fc,

You are given a positive integer $$$x$$$.

You can apply the following operation to the number: remove one occurrence of any digit in such a way that the resulting number does not contain any leading zeroes and is still a positive integer. For example, $$$10142$$$ can be converted to $$$1142$$$, $$$1042$$$, $$$1012$$$ or $$$1014$$$ (note that $$$0142$$$ is not a valid outcome); $$$10$$$ can be converted to $$$1$$$ (but not to $$$0$$$ since it is not positive).

Your task is to find the minimum positive integer that you can obtain from $$$x$$$ if you can apply the aforementioned operation exactly $$$k$$$ times.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^5$$$) — the number of test cases.

The first line of each test case contains a single integer $$$x$$$ ($$$1 \le x \lt 10^{500000}$$$).

The second line contains a single integer $$$k$$$ ($$$0 \le k \lt

Number Reduction

Examples