[Solution] Creep Codeforces Solution | Codeforces Problem Solution 2022

[Solution] Creep Codeforces Solution | Codeforces Problem Solution 2022

A. Creep

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Define the score of some binary string T$T$ as the absolute difference between the number of zeroes and ones in it. (for example, T=$T=$ 010001 contains 4$4$ zeroes and 2$2$ ones, so the score of T$T$ is |4−2|=2$|4-2|=2$).

Define the creepiness of some binary string S$S$ as the maximum score among all of its prefixes (for example, the creepiness of S=$S=$ 01001 is equal to 2$2$ because the score of the prefix S[1…4]$S[1\dots 4]$ is 2$2$ and the rest of the prefixes have a score of 2$2$ or less).

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Given two integers a$a$ and b$b$, construct a binary string consisting of a$a$ zeroes and b$b$ ones with the minimum possible creepiness.

Input

The first line contains a single integer t$t$ (1≤t≤1000)$(1\le t\le 1000)$  — the number of test cases. The description of the test cases follows.

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The only line of each test case contains two integers a$a$ and b$b$ (1≤a,b≤100$1\le a,b\le 100$)  — the numbers of zeroes and ones correspondingly.

Output

For each test case, print a binary string consisting of a$a$ zeroes and b$b$ ones with the minimum possible creepiness. If there are multiple answers, print any of them.