Description

Today is another school day with $n$ classes. The $i$-th class starts at the beginning of minute $l_i$ and ends at the beginning of minute $r_i$.

Little O wants to play basketball during every break between classes. However, the round-trip between the classroom and the playground takes a total of $T$ minutes.

Little O will go to play basketball during a break if and only if he can return to the classroom without being late for the next class. Otherwise, he stays in the classroom.

How many total minutes will Little O spend playing basketball today?

Input Format

• The first line contains two integers $n$ and $T$, representing the number of classes and the round-trip time.
• The next $n$ lines each contain two integers $l_i$ and $r_i$, describing the start and end time of the $i$-th class.

Output Format

Output one integer: the total minutes Little O spends playing basketball.

3 2
1 2
5 7
8 9

1

Hint

Sample #1 Explanation

• Break 1 (between classes 1 and 2): Duration = $5 - 2 = 3$ minutes. After spending $2$ minutes on the round-trip, Little O plays for $1$ minute.
• Break 2 (between classes 2 and 3): Duration = $8 - 7 = 1$ minute. The round-trip requires $2$ minutes, so he skips it.
  Total play time: $1$ minute.

Constraints

• $2 \le n \le 10^5$
• $0 \le T \le 10^8$
• $1 \le l_i \le r_i \le 10^8$
• For $1 \le i \le n-1$: $r_i \le l_{i+1}$ (classes are non-overlapping and ordered chronologically).

Subtasks

• 20%: $n = 2$
• 20%: $T = 0$
• 20%: $T = 1$
• 40%: No additional constraints