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E. Antenna Coverage
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

The mayor of the Central Town wants to modernize Central Street, represented in this problem by the $$$(Ox)$$$ axis.

On this street, there are $$$n$$$ antennas, numbered from $$$1$$$ to $$$n$$$. The $$$i$$$-th antenna lies on the position $$$x_i$$$ and has an initial scope of $$$s_i$$$: it covers all integer positions inside the interval $$$[x_i - s_i; x_i + s_i]$$$.

It is possible to increment the scope of any antenna by $$$1$$$, this operation costs $$$1$$$ coin. We can do this operation as much as we want (multiple times on the same antenna if we want).

To modernize the street, we need to make all integer positions from $$$1$$$ to $$$m$$$ inclusive covered by at least one antenna. Note that it is authorized to cover positions outside $$$[1; m]$$$, even if it's not required.

What is the minimum amount of coins needed to achieve this modernization?

Input

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n \le 80$$$ and $$$n \le m \le 100\ 000$$$).

The $$$i$$$-th of the next $$$n$$$ lines contains two integers $$$x_i$$$ and $$$s_i$$$ ($$$1 \le x_i \le m$$$ and $$$0 \le s_i \le m$$$).

On each position, there is at most one antenna (values $$$x_i$$$ are pairwise distinct).

Output

You have to output a single integer: the minimum amount of coins required to make all integer positions from $$$1$$$ to $$$m$$$ inclusive covered by at least one antenna.

Examples
Input
3 595
43 2
300 4
554 10
Output
281
Input
1 1
1 1
Output
0
Input
2 50
20 0
3 1
Output
30
Input
5 240
13 0
50 25
60 5
155 70
165 70
Output
26
Note

In the first example, here is a possible strategy:

  • Increase the scope of the first antenna by $$$40$$$, so that it becomes $$$2 + 40 = 42$$$. This antenna will cover interval $$$[43 - 42; 43 + 42]$$$ which is $$$[1; 85]$$$
  • Increase the scope of the second antenna by $$$210$$$, so that it becomes $$$4 + 210 = 214$$$. This antenna will cover interval $$$[300 - 214; 300 + 214]$$$, which is $$$[86; 514]$$$
  • Increase the scope of the third antenna by $$$31$$$, so that it becomes $$$10 + 31 = 41$$$. This antenna will cover interval $$$[554 - 41; 554 + 41]$$$, which is $$$[513; 595]$$$

Total cost is $$$40 + 210 + 31 = 281$$$. We can prove that it's the minimum cost required to make all positions from $$$1$$$ to $$$595$$$ covered by at least one antenna.

Note that positions $$$513$$$ and $$$514$$$ are in this solution covered by two different antennas, but it's not important.

In the second example, the first antenna already covers an interval $$$[0; 2]$$$ so we have nothing to do.

Note that the only position that we needed to cover was position $$$1$$$; positions $$$0$$$ and $$$2$$$ are covered, but it's not important.