Maximizing Productivity

문제

Farmer John has $NN$ ($1\le N\le 2\cdot {10}^{5}1\; \backslash leq\; N\; \backslash leq\; 2\; \backslash cdot\; 10^5$) farms, numbered from $11$ to $NN$. It is known that FJ closes farm $ii$ at time $c_{i}c\_i$. Bessie wakes up at time $SS$, and wants to maximize the productivity of her day by visiting as many farms as possible before they close. She plans to visit farm $ii$ on time $t_i+St\_i\; +\; S$. Bessie must arrive at a farm strictly before Farmer John closes it to actually visit it.

Bessie has $QQ$ $(1\le Q\le 2\cdot {10}^5)(1\; \backslash leq\; Q\; \backslash leq\; 2\; \backslash cdot\; 10^5)$ queries. For each query, she gives you two integers $SS$ and $VV$. For each query, output whether Bessie can visit at least $VV$ farms if she wakes up at time $SS$.

입력

The first line consists of $NN$ and $QQ$.

The second line consists of $c_1,c_2,c_3\dots c_{N}c\_1,\; c\_2,\; c\_3\; \backslash dots\; c\_N$ ($1\le c_i\le {10}^{6}1\; \backslash leq\; c\_i\; \backslash leq\; 10^6$).

The third line consists of $t_1,t_2,t_3\dots t_{N}t\_1,\; t\_2,\; t\_3\; \backslash dots\; t\_N$ ($1\le t_i\le {10}^{6}1\; \backslash leq\; t\_i\; \backslash leq\; 10^6$).

The next $QQ$ lines each consist of two integers $VV$ ($1\le V\le N1\; \backslash leq\; V\; \backslash leq\; N$) and $SS$ ($1\le S\le {10}^{6}1\; \backslash leq\; S\; \backslash leq\; 10^6$).

출력

For each of the $QQ$ queries, output YES or NO on a new line.

5 5
3 5 7 9 12
4 2 3 3 8
1 5
1 6
3 3
4 2
5 1

YES
NO
YES
YES
NO