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;
#define N 101000
#define ll long long

struct query {
	int t,s;
}e[N];
int n,m,sgn=-1,k=1;
int T[N];
ll mx,mn,h,X;

void cal(ll &k) {
	if (k>X) k=X;
	if (k<0) k=0;
}

int main()
{
	scanf("%lld%d",&X,&n);
	for (int i=1;i<=n;i++) scanf("%d",&T[i]);
	scanf("%d",&m);
	for (int i=1;i<=m;i++) scanf("%d%d",&e[i].t,&e[i].s);
	
	mn=0; mx=X;
	for (int i=1;i<=m;i++)
	{
		while (k<=n && T[k]<=e[i].t)
		{
			ll v=(T[k]-T[k-1])*sgn;
			mx+=v; mn+=v; h+=v;
			cal(mx); cal(mn);
			sgn*=-1; k++;
		}
		ll now=e[i].s+h,nowh=(e[i].t-T[k-1])*sgn;
		if (now>mx) now=mx;
		if (now<mn) now=mn;
		now+=nowh;
		cal(now);
		printf("%lld\n",now);
	}
	return 0;
}