Largest Kth Value of List - Microsoft Top Interview Questions


Problem Statement :


You are given integers n, total, and k. 

Consider a list of length n whose sum is total and where the absolute difference between any two consecutive numbers in the list is at most 1.

Return the maximum value at index k of such a list.

Constraints

1 ≤ n < 2 ** 31

0 ≤ k < n

0 ≤ total < 2 ** 31

Example 1

Input

n = 3

total = 10

k = 1

Output

4

Explanation

The largest such list is [3, 4, 3].

Example 2

Input

n = 4

total = 10

k = 3

Output

4

Explanation

The largest such list is [1, 2, 3, 4].


Solution :



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                        Solution in C++ :

int solve(int n, int total, int k) {
    long long t = total, nn = n, kk = k;
    return (2 * t + kk * (kk + 1) + (nn - kk - 2) * (nn - kk - 1) + 2 * (nn - kk - 1)) / (2 * nn);
}
                    




                        Solution in Python : 
                            
class Solution:
    def solve(self, n, total, k):
        l = n - k
        diff = total + k * (k + 1) // 2 + l * (l - 1) // 2
        return diff // n


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