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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;

class Solver {
  final int n;
  final int m;
  final int[] as;
  
  Solver(int n, int m, int[] as) {
    this.n = n;
    this.m = m;
    this.as = as;
  }
  
  public long solve() {
    long[] rangeConstants = new long[m + 2];
    long[] rangeFanctors = new long[m + 2];
    for (int i = 1; i < n; i++) {
      if (as[i-1] < as[i]) {
        // x <= a[i-1] + 1 => a[i] - a[i-1]
        // a[i-1] + 1 < x && x <= a[i] => a[i] - x + 1
        // a[i] < x => a[i] - a[i-1]
        
        // x * rangeFanctors[x] + rangeConstants[x]
        rangeConstants[1]          += as[i] - as[i-1];
        rangeConstants[as[i-1] + 1] -= as[i] - as[i-1];
        rangeConstants[as[i-1] + 1] += as[i];
        rangeFanctors [as[i-1] + 1] -= 1;
        rangeConstants[as[i]      ] -= as[i];
        rangeFanctors [as[i]      ] += 1;        
        rangeConstants[as[i]      ] += as[i] - as[i-1];
        
        
      } else {
        // x <= a[i] => a[i] - x + 1
        // a[i] < x && x <= a[i-1] + 1 => m - a[i-1] + 1 + a[i] - 1 => m - a[i-1] + a[i]
        // a[i-1] + 1 < x => a[i] => 1 + m - x + 1 + a[i] - 1 => -x + m + 1 + a[i]
        rangeConstants[1         ] += as[i] + 1;
        rangeFanctors [1         ] -= 1;
        rangeConstants[as[i]   + 1] -= as[i] + 1;
        rangeFanctors [as[i]   + 1] += 1;        
        rangeConstants[as[i]   + 1] += m - as[i-1] + as[i];
        rangeConstants[as[i-1] + 1] -= m - as[i-1] + as[i];
        rangeConstants[as[i-1] + 1] += m + as[i] + 1;
        rangeFanctors [as[i-1] + 1] -= 1;
      }
      
      /*
      {
        long sumConstant = 0;
        long sumFanctor = 0;
        for (int x = 1; x <= m; x++) {
          sumConstant += rangeConstants[x];
          sumFanctor += rangeFanctors[x];
          long count = x * sumFanctor + sumConstant;
          System.err.printf("%3d %3d %3d %3d %3d %3d\n", x, rangeFanctors[x], rangeConstants[x], sumFanctor, sumConstant, count);
        }
      }
      */
    }
    
    long sumConstant = 0;
    long sumFanctor = 0;
    long minCount = Long.MAX_VALUE;
    for (int x = 1; x <= m; x++) {
      sumConstant += rangeConstants[x];
      sumFanctor += rangeFanctors[x];
      long count = x * sumFanctor + sumConstant;
      minCount = Math.min(minCount, count);
    }
    return minCount;
  }
}

public class Main {
  private static void execute(ContestReader reader, PrintWriter out) {
    int n = reader.nextInt();
    int m = reader.nextInt();
    int[] as = reader.nextIntArray(n);
    out.println(new Solver(n, m, as).solve());
  }
  
  public static void main(String[] args) {
    ContestReader reader = new ContestReader(System.in);
    PrintWriter out = new PrintWriter(System.out);
    execute(reader, out);
    out.flush();
  }
}

class ContestReader {
  private BufferedReader reader;
  private StringTokenizer tokenizer;
  
  ContestReader(InputStream in) {
    reader = new BufferedReader(new InputStreamReader(in));
  }
  
  public String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }
  
  public int nextInt() {
    return Integer.parseInt(next());
  }
  
  public long nextLong() {
    return Long.parseLong(next());
  }
  
  public double nextDouble() {
    return Double.parseDouble(next());
  }
  
  public String[] nextArray(int n) {
    String[] array = new String[n];
    for (int i = 0; i < n; i++) {
      array[i] = next();
    }
    return array;
  }
  
  public int[] nextIntArray(int n) {
    int[] array = new int[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextInt();
    }
    return array;
  }
  
  public long[] nextLongArray(int n) {
    long[] array = new long[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextLong();
    }
    return array;
  }
  
  public double[] nextDoubleArray(int n) {
    double[] array = new double[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextDouble();
    }
    return array;
  }
  
  public int[][] nextIntMatrix(int n, int m) {
    int[][] matrix = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextInt();
      }
    }
    return matrix;
  }
  
  public long[][] nextLongMatrix(int n, int m) {
    long[][] matrix = new long[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextLong();
      }
    }
    return matrix;
  }
  
  public double[][] nextDoubleMatrix(int n, int m) {
    double[][] matrix = new double[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextDouble();
      }
    }
    return matrix;
  }
}

class ModCalculator {
  private final long mod;
  
  ModCalculator(long mod) {
    this.mod = mod;
  }
  
  public long add(long a, long b) {
    return (a + b) % mod;
  }
  
  public long mul(long a, long b) {
    return (a * b) % mod;
  }
  
  public long pow(long a, long b) {
    if (b == 0) {
      return 1;
    }
    long v = pow(mul(a, a), b / 2);
    if (b % 2 == 1) {
      return mul(v, a);
    } else {
      return v;
    }
  }
  
  public long inverse(long a) {
    return pow(a, mod - 2);
  }
  
  public long div(long a, long b) {
    return mul(a, inverse(b));
  }
}
 
class ModCombinationCache {
  private final ModCalculator modCalculator;
  private final List<Long> factorialCache;
  private final List<Long> factorialInverseCache;
  
  public ModCombinationCache(ModCalculator modCalculator) {
    this.modCalculator = modCalculator;
    factorialCache = new ArrayList<>();
    factorialCache.add(1L);
    factorialInverseCache = new ArrayList<>();
    factorialInverseCache.add(1L);
  }
  
  private void resize(int n) {
    for (int i = factorialCache.size() - 1; i < n; i++) {
      long v = modCalculator.mul(factorialCache.get(i), i + 1);
      factorialCache.add(v);
      factorialInverseCache.add(modCalculator.inverse(v));
    }
  }
  
  public long getP(int n) {
    resize(n);
    return factorialCache.get(n);
  }
  
  public long getC(int n, int k) {
    resize(n);
    return modCalculator.mul(factorialCache.get(n), modCalculator.mul(factorialInverseCache.get(k), factorialInverseCache.get(n-k)));
  }
}

class Algorithm {
  private static void swap(Object[] list, int a, int b) {
    Object tmp = list[a];
    list[a] = list[b];
    list[b] = tmp;
  }
  
  public static <T extends Comparable<? super T>> boolean nextPermutation(T[] ts) {
    int rightMostAscendingOrderIndex = ts.length - 2;
    while (rightMostAscendingOrderIndex >= 0 &&
        ts[rightMostAscendingOrderIndex].compareTo(ts[rightMostAscendingOrderIndex + 1]) >= 0) {
      rightMostAscendingOrderIndex--;
    }
    if (rightMostAscendingOrderIndex < 0) {
      return false;
    }
    
    int rightMostGreatorIndex = ts.length - 1;
    while (ts[rightMostAscendingOrderIndex].compareTo(ts[rightMostGreatorIndex]) >= 0) {
      rightMostGreatorIndex--;
    }
    
    swap(ts, rightMostAscendingOrderIndex, rightMostGreatorIndex);
    for (int i = 0; i < (ts.length - rightMostAscendingOrderIndex - 1) / 2; i++) {
      swap(ts, rightMostAscendingOrderIndex + 1 + i, ts.length - 1 - i);
    }
    return true;
  }
  
  public static void shuffle(int[] array) {
    Random random = new Random();
    int n = array.length;
    for (int i = 0; i < n; i++) {
      int randomIndex = i + random.nextInt(n - i);
      
      int temp = array[i];
      array[i] = array[randomIndex];
      array[randomIndex] = temp;
    }
  }
  
  public static void shuffle(long[] array) {
    Random random = new Random();
    int n = array.length;
    for (int i = 0; i < n; i++) {
      int randomIndex = i + random.nextInt(n - i);
      
      long temp = array[i];
      array[i] = array[randomIndex];
      array[randomIndex] = temp;
    }
  }
  
  public static void sort(int[] array) {
    shuffle(array);
    Arrays.sort(array);
  }
  
  public static void sort(long[] array) {
    shuffle(array);
    Arrays.sort(array);
  }
}

class UnionFind {
  int[] parents;
  int[] ranks;

  UnionFind(int n) {
    parents = new int[n];
    ranks = new int[n];

    for (int i = 0; i < n; i++) {
      parents[i] = i;
    }
  }

  public int getRoot(int index) {
    if (parents[index] == index) {
      return index;
    } else {
      parents[index] = getRoot(parents[index]);
      return parents[index];
    }
  }

  public boolean sameGroup(int a, int b) {
    return getRoot(a) == getRoot(b);
  }

  public void merge(int a, int b) {
    int rootA = getRoot(a);
    int rootB = getRoot(b);
    if (rootA == rootB) {
      return;
    }
    if (ranks[rootA] < ranks[rootB]) {
      parents[rootA] = rootB;
    } else if (ranks[rootB] < ranks[rootA]) {
      parents[rootB] = rootA;
    } else {
      parents[rootA] = rootB;
      ranks[rootB]++;
    }
  }
}