Alexey has a set of domino pieces of different heights. Deciding to study domino principle in practice, he placed the pieces at different integer points on a coordinate line. Then he chose a particular coordinate. He decided to push the closest domino piece to the left of that coordinate to fall left, and the closest piece to the right of it to fall right. If there is no domino piece to push in some direction, Alexey simply pushed nothing in that direction.
Now he wants to find out how many domino pieces will fall down.
Each domino piece, when falling to the right, will knock down all domino pieces located to the right of it within a distance equal to the height of that piece. Conversely, when falling to the left, it will knock down all domino pieces to the left of it within the same distance.
Thus, if a piece with height $$$H$$$, located at coordinate $$$X$$$, is knocked down to the right, it will knock down all pieces located in the segment $$$[X + 1; X + H]$$$ to the right. If it is knocked down to the left, it will knock down all pieces in the segment $$$[X - H; X - 1]$$$ to the left.
Help Alexey to find out how many domino pieces will fall.
The first line contains two positive integers $$$N$$$ and $$$K$$$ — the number of domino pieces and the coordinate chosen by Alexey respectively ($$$N \leq 10^5; K \leq 10^7;$$$ $$$K$$$ is odd). Each of the following $$$N$$$ lines contains two positive integers $$$X_i$$$ and $$$H_i$$$ — the coordinate and height of the $$$i$$$-th domino piece respectively ($$$X_i, H_i \leq 10^7;$$$ $$$X_i$$$ is even; $$$H_i$$$ is odd). It is guaranteed that the coordinates of all domino pieces are distinct.
Output one number — the total number of domino pieces that will fall down.
3 13 2 5 10 5 6 3
2
5 7 10 3 8 9 14 5 4 3 6 1
4
4 11 2 5 8 3 10 3 6 5
4
In the first example, there are no domino pieces to the right of coordinate $$$K$$$. On the left, Alexey will push the piece at coordinate $$$10$$$. When it falls, it will knock down another piece at coordinate $$$6$$$, but none of the fallen pieces will reach the domino piece at coordinate $$$2$$$.
In the second example, Alexey will push the pieces at coordinates $$$6$$$ and $$$8$$$. The piece at $$$6$$$ does not reach the domino at $$$4$$$ when falling left. However, the piece at $$$8$$$ will knock down two more pieces when falling right.
In the third example, there are no domino pieces to the right of coordinate $$$K$$$. On the left, Alexey will push the piece at coordinate $$$10$$$. When it falls, it will knock down the piece at coordinate $$$8$$$, which will knock down the piece at coordinate $$$6$$$, and that one, in turn, will knock down the piece at coordinate $$$2$$$.
