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<bits/stdc++.h>
using namespace std;

int r[100001],t[100001],a[100001],now,ans,tmp,dir=-1;

int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int X,K;
	cin>>X>>K;
	for(int i=1;i<=K;i++)
		cin>>r[i];
	int q;
	cin>>q;
	for(int i=1;i<=q;i++)
		cin>>t[i]>>a[i];
	int M=X,m=0,t1=0,t2=1;
	while(t2<=q){
		if(t1!=K&&t[t2]>r[t1+1]){
			t1++;
			now=dir*(r[t1]-r[t1-1]);
			M=max(0,min(M+now,X));
			m=max(0,min(m+now,X));
			tmp+=now;dir*=-1;
		}
		else{
			ans=max(m,min(M,a[t2]+tmp));
			ans=max(0,min(X,ans+dir*(t[t2]-r[t1])));
			cout<<ans<<'\n';
			t2++;
		}
	}

}
