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 $\lfloor \frac N A \rfloor = B$ $⌊ \frac{N}{A} ⌋ = B$ and $N \equiv C \pmod A$ $N \equiv C (\mod A)$ .

Constraints

$1 \le Q \le 10^5$ $1 \leq Q \leq 10^{5}$

$1 \le A, B, C \le 10^9$ $1 \leq A, B, C \leq 10^{9}$

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

Copy

1
6 5 11

Sample Output

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Explanation

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

Comments

0

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

what does the $≡$ $\equiv$ 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 $≡$ $\equiv$ 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))