A15483 | Doremy's Number Line
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内存限制256MB
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题目描述
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 $1$ .
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 $1$ .
输入格式
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 $10^5$ .
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 $10^5$ .
输出格式
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).
You can output "YES" and "NO" in any case (for example, strings "yEs", "yes" and "Yes" will be recognized as a positive response).
输入输出样例
输入 #1
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
输出 #1
NO YES YES YES NO YES
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.
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.
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评测结果：Accepted