We have a sandglass consisting of two bulbs, bulb A and bulb B. These bulbs contain some amount of sand. When we put the sandglass, either bulb A or B lies on top of the other and becomes the upper bulb. The other bulb becomes the lower bulb.

The sand drops from the upper bulb to the lower bulb at a rate of 1 gram per second. When the upper bulb no longer contains any sand, nothing happens.

Initially at time 0, bulb A is the upper bulb and contains a grams of sand; bulb B contains X-a grams of sand (for a total of X grams).

We will turn over the sandglass at time r_1,r_2,..,r_K. Assume that this is an instantaneous action and takes no time. Here, time t refer to the time t seconds after time 0.

You are given Q queries. Each query is in the form of (t_i,a_i). For each query, assume that a=a_i and find the amount of sand that would be contained in bulb A at time t_i.

Constraints

* 1≤X≤10^9
* 1≤K≤10^5
* 1≤r_1<r_2< .. <r_K≤10^9
* 1≤Q≤10^5
* 0≤t_1<t_2< .. <t_Q≤10^9
* 0≤a_i≤X (1≤i≤Q)
* All input values are integers.

Input

The input is given from Standard Input in the following format:


X
K
r_1 r_2 .. r_K
Q
t_1 a_1
t_2 a_2
:
t_Q a_Q


Output

For each query, print the answer in its own line.

Examples

Input

180
3
60 120 180
3
30 90
61 1
180 180


Output

60
1
120


Input

100
1
100000
4
0 100
90 100
100 100
101 100


Output

100
10
0
0


Input

100
5
48 141 231 314 425
7
0 19
50 98
143 30
231 55
342 0
365 100
600 10


Output

19
52
91
10
58
42
100

#include <iostream>
#include<vector>
#include<algorithm>
using namespace std;

int main() {
	int x,k;cin>>x>>k;
	vector<int> r(k);
	vector<int> ur(k),dr(k),us(k),ds(k);
	int u=x;
	int d=0;
	int l=-1;
	int exus=0;
	int exds=0;
	int ext=0;
	for(int i=0;i<k;i++){
		cin>>r[i];
		u+=l*(r[i]-ext);
		d+=l*(r[i]-ext);
		if(u>x){
			exus+=u-x;
			u=x;
		}
		if(u<0){
			u=0;
		}
		if(d<0){
			exds+=-d;
			d=0;
		}
		if(d>x){
			d=x;
		}
		ur[i]=u;
		dr[i]=d;
		us[i]=exus;
		ds[i]=exds;
		ext=r[i];
		l*=-1;
	}
//	for(int i=0;i<k;i++){
//		cout<<ur[i]<<' '<<dr[i]<<' '<<us[i]<<' '<<ds[i]<<endl;
//	}
	int q;cin>>q;
	for(int i=0;i<q;i++){
		int t,a;cin>>t>>a;
		int j=upper_bound(r.begin(),r.end(),t)-r.begin();
		int extime,s;
		extime=0;
		s=a;
		if(j){
			extime=r[j-1];
			s=dr[j-1]-ds[j-1]+a;
			if(s<dr[j-1])s=dr[j-1];
			if(s>ur[j-1])s=ur[j-1];
			if(ur[j-1]==dr[j-1])s=ur[j-1];
		}
		s+=((j%2)*2-1)*(t-extime);
		if(s>x)s=x;
		if(s<0)s=0;
		cout<<s<<endl;

	}
	return 0;
}