**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 :

` ````
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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