#include <cstdio>
int r[100005],X,K,Q,a,b,c,d;
void calc(int v){
	c+=v;
	if (a>X-c) a=b=X-c;
		else b=b>X-c?X-c:b;
	if (b<-c) a=b=-c;
		else a=a<-c?-c:a;
}
int main(){
	scanf("%d%d",&X,&K);
	for (int i=1;i<=K;i++) scanf("%d",&r[i]);
	a=0;b=X;c=d=0;
	scanf("%d",&Q);
	for (int i=1,j=1,k=-1;i<=Q;i++){
		int t,x;
		scanf("%d%d",&t,&x);
		for (;j<=K && r[j]<=t;d=r[j++],k=-k) calc(k*(r[j]-d));
		calc(k*(t-d));d=t;
		if (x<a) printf("%d\n",a+c);
			else if (x<=b) printf("%d\n",x+c);
				else printf("%d\n",b+c);
	}
}
### Prompt

Please formulate a cpp solution to the following problem:

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

### Response

```cpp
#include <cstdio>
int r[100005],X,K,Q,a,b,c,d;
void calc(int v){
	c+=v;
	if (a>X-c) a=b=X-c;
		else b=b>X-c?X-c:b;
	if (b<-c) a=b=-c;
		else a=a<-c?-c:a;
}
int main(){
	scanf("%d%d",&X,&K);
	for (int i=1;i<=K;i++) scanf("%d",&r[i]);
	a=0;b=X;c=d=0;
	scanf("%d",&Q);
	for (int i=1,j=1,k=-1;i<=Q;i++){
		int t,x;
		scanf("%d%d",&t,&x);
		for (;j<=K && r[j]<=t;d=r[j++],k=-k) calc(k*(r[j]-d));
		calc(k*(t-d));d=t;
		if (x<a) printf("%d\n",a+c);
			else if (x<=b) printf("%d\n",x+c);
				else printf("%d\n",b+c);
	}
}
```