Divide and Mod

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Points: 3

Time limit: 1.0s

Memory limit: 64M

Author:

uselessleaf

Problem type

Write a program that answers the following question $Q$ ~Q~ times:

Given three integers $A$ ~A~, $B$ ~B~, and $C$ ~C~, find the integer $N$ ~N~ where $\lfloor \frac N A \rfloor = B$ ~\lfloor \frac N A \rfloor = B~ and $N \equiv C \pmod A$ ~N \equiv C \pmod A~.

Constraints

$1 \le Q \le 10^5$ ~1 \le Q \le 10^5~

$1 \le A, B, C \le 10^9$ ~1 \le A, B, C \le 10^9~

Input Specification

The first line contains $Q$ ~Q~. The following $Q$ ~Q~ lines contain 3 integers $A$ ~A~, $B$ ~B~, and $C$ ~C~.

Output Specification

For each question, output on a separate line $N$ ~N~, the integer that satisfies the conditions.

Sample Input

1
6 5 11

Sample Output

Explanation

$N = 35$ ~N = 35~ satisfies both conditions when $A = 6, B = 5, C = 11$ ~A = 6, B = 5, C = 11~: $\lfloor \frac{35}{6} \rfloor = 5$ ~\lfloor \frac{35}{6} \rfloor = 5~, and $35 \equiv 11 \pmod 6$ ~35 \equiv 11 \pmod 6~.

Comments

0

gavin_chen commented on July 20, 2022, 8:16 p.m. ← edited →

what does the $≡$ ~≡~ symbol in the equations mean I looked all around the internet and could not identify what is means other then "identical to" which doesn't explain 35 $≡$ ~≡~ 11. Please help.

3

maxcruickshanks commented on July 22, 2022, 3:33 p.m.

It is a modular congruence symbol.

0

gavin_chen commented on July 26, 2022, 8:19 p.m. ← edited →

Oh that help a lot guess I didn't think BOTH 35 and 11 are moded (and out of all places the answer was it was khan academy (why))