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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <cassert>
#include <cstdlib>
#include <cstring>
#include <utility>
#include <sstream>
#include <limits>
#include <algorithm>
#include <cstdio>
#include <vector>
#include <string>
#include <cctype>
#include <queue>
#include <deque>
#include <stack>
#include <cmath>
#include <ctime>
#include <list>
#include <map>
#include <set>
#define PI (acos(-1.0))
#define Abs(a) (((a)<0) ? (-(a)) :(a) )
#define rep(i,n) for((i)=0;(i)<(n);(i)++)
#define Rep(i,n) for(int i=0;i<(n);i++)
#define Rrep(i,n) for(int i=((n)-1);i>=0;i--)
#define rrep(i,n) for((i)=(n)-1;(i)>=0;(i)--)
#define Pii pair<int,int>
#define PB push_back
#define Size(x) ((int)(x.size()))
using namespace std;
typedef long long mint;
typedef unsigned long long umint;
int main()
{
    //freopen("in.txt","r",stdin);
    int n, t, val;
    cin >> n >> t;
    long long sm = 0;
    mint cen = 0;
    Rep(i,n)
    {
        scanf("%d",&val);
        if(cen <= val)
        {
            sm += t;
            cen = val + t;
        }
        else
        {
            sm += val + t - cen;
            
            cen = val + t;
        }
    }
    cout << sm << endl;
    return 0;
}