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<stdio.h>
#include<algorithm>
using namespace std;
struct que{
	int t;
	int a;
	int wz;
	bool operator<(que b) const
	{
		return t<b.t;
	}
};
que q[262144];
int ans[131072];
int main()
{
	//freopen("c.in","r",stdin);
	//freopen("c.out","w",stdout);
	int x;
	scanf("%d",&x);
	int mn=0,mx=x,inc=0;
	bool isinc=false;
	int n;
	scanf("%d",&n);
	for(int i=0;i<n;i++)
	{
		scanf("%d",&q[i].t);
		q[i].a=-1;
	}
	int m;
	scanf("%d",&m);
	for(int i=0;i<m;i++)
	{
		scanf("%d%d",&q[i+n].t,&q[i+n].a);
		q[i+n].wz=i;
	}
	sort(q,q+n+m);
	int lt=0;
	for(int i=0;i<n+m;i++)
	{
		int dt=q[i].t-lt;
		if(isinc)
		{
			mn+=dt;
			mx+=dt;
			inc+=dt;
			if(mn>x)
			{
				mn=x;
			}
			if(mx>x)
			{
				mx=x;
			}
		}
		else
		{
			mn-=dt;
			mx-=dt;
			inc-=dt;
			if(mn<0)
			{
				mn=0;
			}
			if(mx<0)
			{
				mx=0;
			}
		}
		lt+=dt;
		if(q[i].a<0)
		{
			isinc^=1;
		}
		else
		{
			int answer=q[i].a+inc;
			if(answer<mn)
			{
				answer=mn;
			}
			if(answer>mx)
			{
				answer=mx;
			}
			ans[q[i].wz]=answer;
		}
	}
	for(int i=0;i<m;i++)
	{
		printf("%d\n",ans[i]);
	}
	return 0;
}