Kattis

# Paint Buckets

Gladys runs a paint shop with a huge stock of paint buckets of various volumes and hues. One of the special features of her shop is that she takes orders of any of the $10^9$ colors there are. On the surface of things, this cannot be possible – of course, there is not space enough for at lesat $10^9$ paint buckets!

To solve this problem, Gladys invented a special device capable of changing the hue of a particular color by $1\, 000$ color units. This means that if she gets an order for a particular color $x$, she may instead deliver any of the $2\, 001$ colors $[x - 1\, 000, x + 1\, 000]$.

A slight problem remains though – Gladys old inventory system does not support this particular way of fulfilling orders. Your task is to write her a new system, that determines for a given order of $v$ litres of a particular hue $h$, if the volume of all paint buckets she can transform to hue $h$ is at least $v$ litres.

## Input

The first line of input contains the two integers $1 \le N \le 200\, 000$ and $1 \le Q \le 200\, 000$, the number of paint buckets and the number of orders the system will get. This is followed by $N$ lines describing the paint buckets. The $i$’th of these lines contains the positive integers $h_ i$ ($1 \le h_1 \le 10^9$) and $v_ i$ ($1 \le v_ i \le 10^4$), the hue and volume of the $i$’th bucket.

Finally, $Q$ lines follow containing the paint orders. The $i$’th of these lines contains the positive integers $h_ i$ ($1 \le h_1 \le 10^9$) and $v_ i$ ($1 \le v_ i \le 10^4$), the hue and volume of the $i$’th order.

## Output

For each order $h$, $v$, output yes if Gladys can fullfill the order, and no otherwise.

Sample Input 1 Sample Output 1
9 6
5000000 100
5001000 100
5002000 100
6000000 100
6001000 100
6002001 100
7000000 100
7001001 100
7002001 100
5001000 301
5001000 300
6001000 201
6001000 200
7001001 201
7001001 200

no
yes
no
yes
no
yes