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

• $1 \leq N \leq 200,000$
• $1 \leq T \leq 10^9$
• $0 = t_1 < t_2 < t_3 < , ..., < t_{N-1} < t_N \leq 10^9$
• $T$ 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 $X$.

2 4
0 3

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.

2 4
0 5

8

One second after the shower stops emission of water triggered by the first person, the switch is pushed again.

4 1000000000
0 1000 1000000 1000000000

2000000000

1 1
0

1

9 10
0 3 5 7 100 110 200 300 311

67