Doremy's Number Line
Description
Doremy has two arrays $a$ and $b$ of $n$ integers each, and an integer $k$.
Initially, she has a number line where no integers are colored. She chooses a permutation $p$ of $[1,2,\ldots,n]$ then performs $n$ moves. On the $i$-th move she does the following:
- Pick an uncolored integer $x$ on the number line such that either:
- $x \leq a_{p_i}$; or
- there exists a colored integer $y$ such that $y \leq a_{p_i}$ and $x \leq y+b_{p_i}$.
- Color integer $x$ with color $p_i$.
Determine if the integer $k$ can be colored with color $1$.
The input consists of multiple test cases. The first line contains a single integer $t$ ($1\le t\le 10^4$) — the number of test cases. The description of the test cases follows.
The first line contains two integers $n$ and $k$ ($1 \le n \le 10^5$, $1 \le k \le 10^9$).
Each of the following $n$ lines contains two integers $a_i$ and $b_i$ ($1 \le a_i,b_i \le 10^9$).
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.
For each test case, output "YES" (without quotes) if the point $k$ can be colored with color $1$. Otherwise, output "NO" (without quotes).
You can output "YES" and "NO" in any case (for example, strings "yEs", "yes" and "Yes" will be recognized as a positive response).
Input
The input consists of multiple test cases. The first line contains a single integer $t$ ($1\le t\le 10^4$) — the number of test cases. The description of the test cases follows.
The first line contains two integers $n$ and $k$ ($1 \le n \le 10^5$, $1 \le k \le 10^9$).
Each of the following $n$ lines contains two integers $a_i$ and $b_i$ ($1 \le a_i,b_i \le 10^9$).
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.
Output
For each test case, output "YES" (without quotes) if the point $k$ can be colored with color $1$. Otherwise, output "NO" (without quotes).
You can output "YES" and "NO" in any case (for example, strings "yEs", "yes" and "Yes" will be recognized as a positive response).
6
4 16
5 3
8 12
10 7
15 1
4 16
8 12
10 7
15 1
5 3
4 16
10 7
15 1
5 3
8 12
4 16
15 1
5 3
8 12
10 7
1 1000000000
500000000 500000000
2 1000000000
1 999999999
1 1
NO
YES
YES
YES
NO
YES
Note
For the first test case, it is impossible to color point $16$ with color $1$.
For the second test case, $p=[2,1,3,4]$ is one possible choice, the detail is shown below.
- On the first move, pick $x=8$ and color it with color $2$ since $x=8$ is uncolored and $x \le a_2$.
- On the second move, pick $x=16$ and color it with color $1$ since there exists a colored point $y=8$ such that $y\le a_1$ and $x \le y + b_1$.
- On the third move, pick $x=0$ and color it with color $3$ since $x=0$ is uncolored and $x \le a_3$.
- On the forth move, pick $x=-2$ and color it with color $4$ since $x=-2$ is uncolored and $x \le a_4$.
- In the end, point $-2,0,8,16$ are colored with color $4,3,2,1$, respectively.
For the third test case, $p=[2,1,4,3]$ is one possible choice.
For the fourth test case, $p=[2,3,4,1]$ is one possible choice.