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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<ll>;
using vii = vector<vi>;
using Pll = pair<ll, ll>;
#define rep(i,n) for(ll i=0;i<(ll)(n);i++)
#define all(v) v.begin(), v.end()
#define sz(x) ((int) x.size())
#define pb push_back
#define mp make_pair
#define mt make_tuple
#define F first
#define S second
const int MOD = 1e9+7;
const int INF = 2e9;
template<class T> void print(const T& t){ cout << t << endl; }
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
int gcd(int a,int b){return b?gcd(b,a%b):a;}

int main(){
  ll n, t;
  cin>>n>>t;
  ll ans = 34;
  vi a(n);
  rep(i,n){
    cin >> a[i];
    ans += t;
    if(a[i]-a[i-1]<t){
      ans -= t - (a[i] - a[i - 1]);
    }
  }
  ans += t;
  print(ans);
}