## GUPTA MECHANICAL

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## [Solution] Creep Codeforces Solution

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

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

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

Input

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

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

Output

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