codeforce B. Chloe and the sequence (递归)


Chloe, the same as Vladik, is a competitive programmer. She didn't have any problems to get to the olympiad like Vladik, but she was confused by the task proposed on the olympiad.

Let's consider the following algorithm of generating a sequence of integers. Initially we have a sequence consisting of a single element equal to 1. Then we perform (n - 1) steps. On each step we take the sequence we've got on the previous step, append it to the end of itself and insert in the middle the minimum positive integer we haven't used before. For example, we get the sequence [1, 2, 1] after the first step, the sequence [1, 2, 1, 3, 1, 2, 1] after the second step.

The task is to find the value of the element with index k (the elements are numbered from 1

### Codeforces Problem 797B Explanation The problem titled "Restoring the Permutation" requires reconstructing a permutation from its prefix sums modulo \( m \). Given an array of integers representing these prefix sums, one must determine whether it is possible to restore such a permutation. In this context, a **permutation** refers to an ordered set containing each integer exactly once within a specified range. The task involves checking if there exists any valid sequence that matches the provided conditions when performing operations as described in the problem statement[^1]. To solve this issue effectively: - Iterate through all elements while maintaining two variables: `current_sum` which tracks cumulative sum during iteration; and `min_value`, used later for adjustments. ```cpp int n, m; cin >> n >> m; vector<int> s(n); for (auto& x : s) cin >> x; ``` Calculate differences between consecutive terms after adjusting initial values appropriately by subtracting minimum value found so far at every step. This adjustment ensures non-negativity throughout calculations without altering relative order among elements. Check feasibility based on properties derived from constraints given in the question text. Specifically, ensure no duplicate residues appear under modulus operation since they would violate uniqueness required for permutations. Finally, construct answer using adjusted difference list obtained previously along with necessary checks ensuring correctness according to rules outlined above.
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