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++11 (GCC 4.8.1) (judge verdict: Accepted)

#include <algorithm>
#include <array>
#include <bitset>
#include <complex>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <set>
#include <stack>
#include <unordered_map>
#include <unordered_set>
#include <queue>

using namespace std;

struct BoolName : numpunct<char> {
  string t, f;
  BoolName (string t = "Yes", string f = "No") : t(t), f(f) {}
  string do_truename() const {return t;}
  string do_falsename() const {return f;}
};

struct Initializer {
  Initializer() {
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout << fixed << setprecision(15) << boolalpha;
    cout.imbue(locale(cout.getloc(), new BoolName));
  }
} initializer;

template<typename T> istream& operator>>(istream &s, vector<T> &v) {
  for (T &t : v) s >> t;
  return s;
}

template<typename T> ostream& operator<<(ostream &s, const vector<T> &v) {
  for (const T &t : v) s << t << endl;
  return s;
}

int main() {
  int n, T;
  cin >> n >> T;
  vector<int> t(n);
  cin >> t;
  int s = T;
  for (int i = 1; i < n; ++i) s += min(T, t[i] - t[i - 1]);
  cout << s << endl;
}