The Clock
Description
Victor has a 24-hour clock that shows the time in the format "HH:MM" (00 $\le$ HH $\le$ 23, 00 $\le$ 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 03:12, 09:12, 15:12, 21:12, 03:12, 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 12:21, 05:50, 11:11 are palindromes but 13:13, 22:10, 02:22 are not.
The first line of the input contains an integer $t$ ($1 \leq t \leq 100$) — 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 "59" (both "HH" and "MM" have exactly two digits) and an integer $x$ ($1 \leq x \leq 1440$) — the number of minutes Victor takes to look again at the clock.
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 $s$.
Input
The first line of the input contains an integer $t$ ($1 \leq t \leq 100$) — 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 "59" (both "HH" and "MM" have exactly two digits) and an integer $x$ ($1 \leq x \leq 1440$) — 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 $s$.
Samples
6
03:12 360
00:00 1
13:22 2
15:15 10
11:11 1440
22:30 27
1
16
10
0
1
1
Note
The first test case is explained in the statement.