Merge branch 'opencodeiiita:main' into main

Author: ishantripathi64

Problems/Mathematics/Day-02/q002.md

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+## Problem Description
+
+Masha works in an advertising agency. In order to promote a new brand, she wants to conclude contracts with some bloggers.
+
+Masha has connections with `n` different bloggers. Blogger numbered `i` has `ai` followers.
+
+Due to a limited budget, Masha can only sign contracts with `k` different bloggers. She wants the advertisement to be seen by as many people as possible, so she must choose bloggers such that the **total number of followers is maximized**.
+
+Your task is to find the **number of ways** to select `k` bloggers so that the total number of their followers is maximum possible.
+
+Two ways are considered different if there is at least one blogger selected in one way but not in the other.
+
+---
+
+## Input Format
+
+- The first line contains an integer `t` — the number of test cases.
+- For each test case:
+  - The first line contains two integers `n` and `k`
+  - The second line contains `n` integers `a1, a2, ..., an`, where `ai` is the number of followers of the `i`-th blogger
+
+---
+
+## Output Format
+
+- For each test case, print a single integer — the number of ways to select `k` bloggers such that the total number of followers is maximum possible.
+- Since the answer can be large, print it modulo `10^9 + 7`.
+
+---
+
+
+
+## Constraints
+
+- `1 ≤ t ≤ 1000`
+- `1 ≤ k ≤ n ≤ 1000`
+- `1 ≤ ai ≤ n`
+- The sum of `n` over all test cases does not exceed `1000`
+
+---
+
+## Sample Input
+
+```
+3
+4 3
+1 3 1 2
+4 2
+1 1 1 1
+2 1
+1 2
+```
+---
+
+## Output
+
+```
+2
+6
+1
+```
+
+---
+
+### Additional Resource
+
+For understanding **modular arithmetic and modular inverses**, which are useful for solving problems with answers modulo `10^9+7`, you can check this video:  
+https://youtu.be/RCq5TYMZEwg
+
+---
+
+
+[PROBLEM LINK](http://codeforces.com/contest/1475/problem/E)

Problems/Mathematics/Day-02/q003.md

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+## Problem Description
+
+You are given a single integer `N`.
+
+You are asked to compute the following summation:
+
+Σ(i=1 to N) Σ(j=1 to N) Σ(k=1 to i) Σ(l=1 to j) (gcd(k, i) × gcd(l, j) × gcd(i, j))
+
+Output the value of this summation **modulo 1000000007**.
+
+---
+
+## Input Format
+
+- The input consists of a single integer `N`.
+
+---
+
+## Output Format
+
+- Output the value of the summation modulo `1000000007`.
+
+---
+
+## Constraints
+
+- 1 ≤ N ≤ 10^6
+
+---
+
+
+## Sample Input 1
+
+```
+2
+```
+---
+
+## Output
+
+```
+25
+```
+---
+
+## Sample Input 2
+
+```
+8
+```
+---
+
+## Output
+
+```
+13348
+```
+---
+
+[PROBLEM LINK](https://www.codechef.com/problems/YETGCD?tab=statement)