Problem:
Score : 700 points

Problem Statement

Snuke is buying a lamp.
The light of the lamp can be adjusted to m levels of brightness, represented by integers from 1 through m, by the two buttons on the remote control.

The first button is a "forward" button. When this button is pressed, the brightness level is increased by 1, except when the brightness level is m, in which case the brightness level becomes 1.

The second button is a "favorite" button. When this button is pressed, the brightness level becomes the favorite brightness level x, which is set when the lamp is purchased.

Snuke is thinking of setting the favorite brightness level x so that he can efficiently adjust the brightness.
He is planning to change the brightness n-1 times. In the i-th change, the brightness level is changed from a_i to a_{i+1}. The initial brightness level is a_1.
Find the number of times Snuke needs to press the buttons when x is set to minimize this number.

Constraints

2 \leq n,m \leq 10^5

1 \leq a_i\leq m

a_i \neq a_{i+1}

n, m and a_i are integers.

Input

Input is given from Standard Input in the following format:

n m
a_1 a_2 … a_n

Output

Print the minimum number of times Snuke needs to press the buttons.

Sample Input 1

4 6
1 5 1 4

Sample Output 1

5

When the favorite brightness level is set to 1, 2, 3, 4, 5 and 6, Snuke needs to press the buttons 8, 9, 7, 5, 6 and 9 times, respectively.
Thus, Snuke should set the favorite brightness level to 4.
In this case, the brightness is adjusted as follows:

In the first change, press the favorite button once, then press the forward button once.

In the second change, press the forward button twice.

In the third change, press the favorite button once.

Sample Input 2

10 10
10 9 8 7 6 5 4 3 2 1

Sample Output 2

45

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

#define fs first
#define sc second
#define pb emplace_back
#define mp make_pair
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)

using pii = pair<int, int>;
using vi = vector<int>;
using lint = long long;

const int inf = 1001001001;
const lint linf = 1001001001001001001ll;
const int mod = 1e9 + 7;
const int dx[]{0, 1, 0, -1, -1, -1, 1, 1}, dy[]{1, 0, -1, 0, -1, 1, -1, 1};

template<typename T> inline bool chmin(T &a, T b) { if (a > b) { a = b; } return a > b; }
template<typename T> inline bool chmax(T &a, T b) { if (a < b) { a = b; } return a < b; }
template<typename T> inline void print(const T &x, string s = "\n") { cout << x << s; }
template<typename T> inline void print(const vector<T> &v, string s = " ") 
{ if (!v.size()) puts(""); rep(i, v.size()) cout << v[i] << (i + 1 == v.size() ? "\n" : s); }
inline bool inside(int y, int x, int H, int W) { return 0 <= y && y < H && 0 <= x && x < W; }
inline lint in() { lint x; std::cin>>x; return x; }

int n, m;
vi a;

inline lint diff(int x, int y) {
	if (y < x) y += m;
	return y - x;
}

inline lint mini(int x, int y, int fav) {
	return min(diff(x, y), diff(fav, y) + 1);
}

lint ans(int fav) {
	int ret = 0;
	for (int i = 1; i < n; ++i) {
		ret += mini(a[i - 1], a[i], fav);
	}

	return ret;
}

signed main() {
	cin >> n >> m;
	rep(i, n) a.pb(in() - 1);

	// [l, r)
	int l = 0, r = min(m / 2 + 100, m);
	while (r - l > 500) {
		int lch = (l * 2 + r) / 3;
		int rch = (l + r * 2) / 3;

		int v = ans(lch), u = ans(rch);

		if (v < u) {
			r = rch;
		} else {
			l = lch;
		}
	}

	//cout << l << " " << r << endl;
	lint beet = inf;
	for (int i = l; i <= r; ++i) {
		lint cnt = ans(i);
		//if (ans > cnt) cout << i << " " << cnt << endl;
		chmin(beet, cnt); 
	}

	// [l, r)
	l = max(m / 2 - 100, 0), r = m;
	while (r - l > 500) {
		int lch = (l * 2 + r) / 3;
		int rch = (l + r * 2) / 3;

		int v = ans(lch), u = ans(rch);

		if (v > u) {
			r = rch;
		} else {
			l = lch;
		}
	}
	for (int i = l; i <= r; ++i) {
		lint cnt = ans(i);
		//if (ans > cnt) cout << i << " " << cnt << endl;
		chmin(beet, cnt); 
	}
	/*
	for (int i = 0; i < m; ++i) {
		cout << ans(i) << endl;
	}
*/
	print(beet);
}