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## [Solution] The Clock Codeforces Solution | Codeforces Problem Solution 2022

D. The Clock
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Victor has a 24-hour clock that shows the time in the format "HH:MM" (00 $\le$ HH $\le$ 2300 $\le$ MM $\le$ 59). He looks at the clock every $x$ minutes, and the clock is currently showing time $s$.

How many different palindromes will Victor see in total after looking at the clock every $x$ minutes, the first time being at time $s$?

For example, if the clock starts out as 03:12 and Victor looks at the clock every $360$ minutes (i.e. every $6$ hours), then he will see the times 03:1209:1215:1221:1203:12, and the times will continue to repeat. Here the time 21:12 is the only palindrome he will ever see, so the answer is $1$.

A palindrome is a string that reads the same backward as forward. For example, the

times 12:2105:5011:11 are palindromes but 13:1322:1002:22 are not.

Input

The first line of the input contains an integer $t$ ($1\le t\le 100$) — the number of test cases. The description of each test case follows.

The only line of each test case contains a string $s$ of length $5$ with the format "HH:MM" where "HH" is from "00" to "23" and "MM" is from "00" to "50" (both "HH" and "MM" have exactly two digits) and an integer $x$ ($1\le x\le 1440$) — the number of minutes Victor takes to look again at the clock.

Output

For each test case, output a single integer — the number of different palindromes Victor will see if he looks at the clock every $x$ minutes starting from time $s$.