K. Smoke Bombs on the Moor
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Watson runs along a straight road from position $$$0$$$ to the Palace at position $$$L$$$.

  • Watson runs with constant speed $$$v$$$.
  • The Hound starts behind Watson at position $$$-S$$$ and runs with constant speed $$$k \cdot v$$$.
  • There are $$$n$$$ smoke bombs on the road. Bomb $$$i$$$ is located at position $$$p_i$$$ and has a duration $$$b_i$$$ seconds.

Watson runs only forward (toward increasing positions), and the Hound always runs forward as well.

Smoke Bombs When Watson reaches position $$$p_i$$$, he immediately picks up bomb $$$i$$$ (this takes no time). At any later moment, Watson may use any bomb he has already picked up. When Watson uses bomb $$$i$$$, the Hound stops moving for exactly $$$b_i$$$ seconds, while Watson continues running normally. Each bomb can be used at most once, and Watson may use at most $$$T$$$ bombs total. If Watson uses a bomb while the Hound is already stopped, the remaining stop time increases accordingly.

Capture rule Watson is caught if the Hound reaches Watson before Watson reaches the Palace.

Watson is considered safe if he reaches the Palace before the Hound catches him, or if their first meeting happens exactly at the Palace gates (position $$$L$$$).

Task Determine whether Watson can reach the Palace safely.

Input

The first line contains six integers $$$n, L, S, v, k, T$$$: $$$ 1 \le n \le 2\cdot 10^5,\quad 1 \le L \le 10^9,\quad 1 \le S \le 10^9,\quad 1 \le v \le 3000,\quad 1 \le k \le 1000,\quad 0 \le T \le n. $$$ Each of the next $$$n$$$ lines contains two integers $$$p_i$$$ and $$$b_i$$$: $$$ 0 \le p_i \le L,\quad 0 \le b_i \le 10^9. $$$ Multiple bombs may be located at the same position.

Output

Print YES if Watson can reach the Palace safely, otherwise print NO.

Example
Input
3 10 6 1 2 2
3 1
6 2
9 2
Output
YES