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 9.2.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
typedef long long ll;
#define rep(i,n) for(int i=0; i<(int)(n); i++)
int upcmpii(const void *a, const void *b){
    return (*(int*)a == *(int*)b ? 0 : (*(int*)a > *(int*)b ? 1 : -1));
}
void sort_ui(int *a, int n){ qsort(a, n, sizeof(int), upcmpii); }

int main(){
    int n, t; scanf("%d%d",&n,&t);
    int a[202020];
    rep(i,n) scanf("%d",a+i);
    sort_ui(a,n);
    ll ans = t, tmp = a[0]+t;
    rep(i,n-1){
        if(tmp >= a[i+1]){
            ans += a[i+1] - a[i];
        }else{
            ans += t;
        }
        tmp = a[i+1] + t;
    }
    
    printf("%lld\n",ans);
}