Problem:
Score : 300 points

Problem Statement

In a public bath, there is a shower which emits water for T seconds when the switch is pushed.

If the switch is pushed when the shower is already emitting water, from that moment it will be emitting water for T seconds.
Note that it does not mean that the shower emits water for T additional seconds.

N people will push the switch while passing by the shower.
The i-th person will push the switch t_i seconds after the first person pushes it.

How long will the shower emit water in total?

Constraints

1 ≤ N ≤ 200,000

1 ≤ T ≤ 10^9

0 = t_1 < t_2 < t_3 < , ..., < t_{N-1} < t_N ≤ 10^9

T and each t_i are integers.

Input

Input is given from Standard Input in the following format:

N T
t_1 t_2 ... t_N

Output

Assume that the shower will emit water for a total of X seconds. Print X.

Sample Input 1

2 4
0 3

Sample Output 1

7

Three seconds after the first person pushes the water, the switch is pushed again and the shower emits water for four more seconds, for a total of seven seconds.

Sample Input 2

2 4
0 5

Sample Output 2

8

One second after the shower stops emission of water triggered by the first person, the switch is pushed again.

Sample Input 3

4 1000000000
0 1000 1000000 1000000000

Sample Output 3

2000000000

Sample Input 4

1 1
0

Sample Output 4

1

Sample Input 5

9 10
0 3 5 7 100 110 200 300 311

Sample Output 5

67

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

int check_input(int N, int T, int* t)
{
  if((1 <= N && N <= 200000) && (1 <= T && T <= 1000000000)){
    int i,temp,flag;
    temp = 0;
    flag = 1;
    for(i = 0; i < N; i++){
      if(temp > t[i] && temp != 0){
        flag = -1;
        puts("Error: tの制約条件を満たしていません");
        break;
      }
      temp = t[i];
    }
    return flag;
  }else{
    puts("Error: N,Tの制約条件を満たしていません");
    return -1;
  }
}

int solution(int N, int T, int* t)
{
  int i,sum;
  sum = 0;
  for(i = 0; i < N-1; i++){
    if(t[i+1] - t[i] < T){
      sum += t[i+1] - t[i];
    }else{
      sum += T;
    }
  }
  return sum+T;
}

int main()
{
  int N,T,i;
  char line[256], *ch;
  scanf("%d %d", &N, &T);
  int t[N];
  for(i=0; i < N; i++){
    scanf("%d", &t[i]);
  }
  if (check_input(N, T, t) == 1){
    int time = solution(N,T,t);
    printf("%d\n", time);
    return 0;
  }
  else{
    return -1;
  }

}