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 <cstdio>
#include <algorithm>
using namespace std;
const int maxn=1e5+10;

int x,k,a,b,c,r[maxn];
int q,t[maxn],g[maxn];

int main()
{
	scanf("%d%d",&x,&k);
	for(int i=1;i<=k;i++) scanf("%d",&r[i]);
	r[0]=0;r[k+1]=1e9+10;
	scanf("%d",&q);
	for(int i=1;i<=q;i++) scanf("%d%d",&t[i],&g[i]);
	int pos=1;
	
	a=0;b=x;c=0;
	for(int i=0;i<=k;i++)
	{
		while(pos<=q && t[pos]<=r[i+1])
		{
			g[pos]=max(g[pos],a);
			g[pos]=min(g[pos],b);
			g[pos]+=c;
			if (i%2) g[pos]+=t[pos]-r[i];
			else g[pos]-=t[pos]-r[i];
			g[pos]=max(g[pos],0);
			g[pos]=min(g[pos],x);
			
			printf("%d\n",g[pos]);
			pos++;
		}
		
		int tmp=r[i+1]-r[i];
		if (i%2)
		{
			c+=tmp;
			if (b+c>x)
			{
				if (a+c<=x) b=x-c;
				else
				{
					a=0;b=0;
					c=x;
				}
			}
		}
		else
		{
			c-=tmp;
			if (a+c<0) 
			{
				if (b+c>=0) a=-c;
				else 
				{
					a=0;b=0;
					c=0;
				}	 
			}
		}
	}
	
	return 0;
}