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<algorithm>
#include<vector>
#include<queue>
#define lol(i,n) for(int i=0;i<n;i++)
#define mod 1000000007
typedef long long ll;
using namespace std;
int x,k,r[100010],q,a,t;
int main(){
	cin>>x>>k;
	r[0]=0;
	lol(i,k)cin>>r[i+1];
	cin>>q;
	int pnt=1;
	int left=0,right=x,nowleft=0,nowright=x;
	while(q--){
		cin>>t>>a;
		while(pnt<=k){
			if(r[pnt]>t)break;
			int move;
			if(pnt%2==0)move=+(r[pnt]-r[pnt-1]);
			if(pnt%2==1)move=-(r[pnt]-r[pnt-1]);
			nowleft+=move,nowright+=move;
			right-=max(0,nowright-x);
			left+=max(0,0-nowleft);
			if(left>right)left=right;
			nowleft=max(0,nowleft);
			nowleft=min(x,nowleft);
			nowright=max(0,nowright);
			nowright=min(x,nowright);
			//cout<<r[pnt]<<"#"<<pnt<<" "<<left<<" "<<right<<" "<<nowleft<<" "<<nowright<<endl;
			pnt++;
		}
		int lastref;
		if(a<=left)lastref=nowleft;
		if(left<a&&a<right)lastref=nowleft+a-left;
		if(right<=a)lastref=nowright;
		if(pnt%2==0)lastref+=(t-r[pnt-1]);
		if(pnt%2==1)lastref-=(t-r[pnt-1]);
		lastref=max(0,lastref);
		lastref=min(x,lastref);
		//cout<<"%"<<left<<" "<<right<<" "<<a<<" "<<nowleft<<" "<<nowright<<endl;
		cout<<lastref<<endl;
	}
	return 0;
}
