P1956 Sum

Given a sequence $a_1, a_2, \cdots, a_n$ and $k, p$. Let $S_{i,j}=\sum\limits_{k=i}^j a_k$, then: $$\mathit{Answer}=\min\{S_{i,j}\bmod p\ |\ S_{i,j}\bmod p\ge k\}$$ where $i \le j$, and $\{S_{i,j}\bmod p\ |\ S_{i,j}\bmod p\ge k\}\ne\varnothing$.

The first line contains three positive integers $n, k, p$. The second line contains $n$ positive integers, denoting $a_1, a_2, \cdots, a_n$.

Output one positive integer on a single line, which is $\mathit{Answer}$.

### Constraints For $100\%$ of the testdata, $1\le n\le10^5$, $1\le k,p,a_i\le10^{18}$. Translated by ChatGPT 5