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 (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define FOR(i, a, b) for(i = a; i < b; ++i)
#define REP(i, n) FOR(i, 0, n)
#define comp(a, b) comp(const void *a, const void *b)
#define MOD  1000000007

typedef unsigned int uint;
typedef unsigned long ulong;
typedef unsigned long long ull;

void TF_print(char boolean, char T[], char F[]){
    if(boolean){
        printf("%s\n", T);
    }else{
        printf("%s\n", F);
    }
}

int main(){
    ull ANS = 0, stopT = 0, T, t;
    uint N;
    scanf("%u %llu", &N, &T);
    uint i;
    REP(i, N){
        scanf("%llu", &t);
        if(stopT < t){
            ANS += T;
            stopT = t + T;
        }else{
            ANS += (T + t - stopT);
            stopT = t + T;
        }
    }
    printf("%llu\n", ANS);
    return 0;
}