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 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <inttypes.h>

static inline int_fast64_t max(int_fast64_t a, int_fast64_t b)
{
    return (a >= b) ? a : b;
}

int main(void)
{
    int_fast64_t n, t;
    scanf("%" SCNdFAST64" %" SCNdFAST64, &n, &t);
    int_fast64_t total = 0, tmp1 = 0, tmp2 = 0;
    for (int_fast64_t i = 0; i < n; ++i) {
        tmp1 = tmp2;
        scanf("%" SCNdFAST64, &tmp2);
        if (i > 0) {
            total += max(t - (tmp2 - tmp1), 0);
        }
    }
    printf("%" PRIdFAST64 "\n", n * t - total);
    return 0;
}