A. Orders
time limit per test
1 second
memory limit per test
1024 megabytes
input
standard input
output
standard output

A factory receives $$$n$$$ orders at the beginning of day $$$1$$$. The $$$i$$$-th order can be described as two integers $$$a_i$$$ and $$$b_i$$$, indicating that at the end of day $$$a_i$$$, the factory needs to deliver $$$b_i$$$ products to the customer.

Given that the factory can produce $$$k$$$ products each day, and at the beginning of day $$$1$$$ the factory has no product in stock, can the factory complete all orders?

Input

There are multiple test cases. The first line of the input contains an integer $$$T$$$ ($$$1 \le T \le 100$$$) indicating the number of test cases. For each test case:

The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 100$$$, $$$1 \le k \le 10^9$$$) indicating the number of orders and the number of products the factory can produce each day.

For the following $$$n$$$ lines, the $$$i$$$-th line contains two integers $$$a_i$$$ and $$$b_i$$$ ($$$1 \le a_i, b_i \le 10^9$$$) indicating that the $$$i$$$-th order require the factory to deliver $$$b_i$$$ products at the end of day $$$a_i$$$.

Output

For each test case output one line. If the factory can complete all orders output Yes, otherwise output No.

Example
Input
2
4 5
6 12
1 3
6 15
8 1
3 100
3 200
4 300
6 100
Output
Yes
No
Note

For the first sample test case, the factory can produce $$$5$$$ products each day.

  • At the end of day $$$1$$$, there are $$$5$$$ products in stock so the factory can complete the $$$2$$$-nd order. After delivery, there are $$$2$$$ products left in stock.
  • At the end of day $$$6$$$, the factory produces $$$25$$$ more products. There are $$$27$$$ products in stock so the factory can complete the $$$1$$$-st and the $$$3$$$-rd order. After delivery, there are $$$0$$$ products left in stock.
  • At the end of day $$$8$$$, the factory produces $$$10$$$ more products. There are $$$10$$$ products in stock so the factory can complete the $$$4$$$-th order. After delivery, there are $$$9$$$ products left in stock.

For the second sample test case, the factory can produce $$$100$$$ products each day.

  • At the end of day $$$3$$$, there are $$$300$$$ products in stock and the factory can complete the $$$1$$$-st order. After delivery, there are $$$100$$$ products left in stock.
  • At the end of day $$$4$$$, the factory produces $$$100$$$ more products. There are only $$$200$$$ products in stock so the factory cannot complete the $$$2$$$-nd order.