#P1168A. Increasing by Modulo
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ID: 1970
Type: RemoteJudge
2000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: 5
Uploaded By:
Hydro
Tags> Increasing by Modulo
Description
Toad Zitz has an array of integers, each integer is between $0$ and $m-1$ inclusive. The integers are $a_1, a_2, \ldots, a_n$.
In one operation Zitz can choose an integer $k$ and $k$ indices $i_1, i_2, \ldots, i_k$ such that $1 \leq i_1 < i_2 < \ldots < i_k \leq n$. He should then change $a_{i_j}$ to $((a_{i_j}+1) \bmod m)$ for each chosen integer $i_j$. The integer $m$ is fixed for all operations and indices.
Here $x \bmod y$ denotes the remainder of the division of $x$ by $y$.
Zitz wants to make his array non-decreasing with the minimum number of such operations. Find this minimum number of operations.
The first line contains two integers $n$ and $m$ ($1 \leq n, m \leq 300\,000$) — the number of integers in the array and the parameter $m$.
The next line contains $n$ space-separated integers $a_1, a_2, \ldots, a_n$ ($0 \leq a_i < m$) — the given array.
Output one integer: the minimum number of described operations Zitz needs to make his array non-decreasing. If no operations required, print $0$.
It is easy to see that with enough operations Zitz can always make his array non-decreasing.
Input
The first line contains two integers $n$ and $m$ ($1 \leq n, m \leq 300\,000$) — the number of integers in the array and the parameter $m$.
The next line contains $n$ space-separated integers $a_1, a_2, \ldots, a_n$ ($0 \leq a_i < m$) — the given array.
Output
Output one integer: the minimum number of described operations Zitz needs to make his array non-decreasing. If no operations required, print $0$.
It is easy to see that with enough operations Zitz can always make his array non-decreasing.
Samples
5 3
0 0 0 1 2
0
5 7
0 6 1 3 2
1
Note
In the first example, the array is already non-decreasing, so the answer is $0$.
In the second example, you can choose $k=2$, $i_1 = 2$, $i_2 = 5$, the array becomes $[0,0,1,3,3]$. It is non-decreasing, so the answer is $1$.