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;

int x,k,q,r[100010],t[100010],a[100010];

void work()
{
	scanf("%d %d",&x,&k);
	for (int i=1; i<=k; i++)  scanf("%d",&r[i]);
	scanf("%d",&q);
	for (int i=1; i<=q; i++)  scanf("%d %d",&t[i],&a[i]);
	if (t[q]>=r[k])  r[++k]=t[q]+1;
	for (int i=1,j=1,L=0,R=x,s=0,ty=-1; i<=k; i++,ty*=-1)
		{
			for (; (j<=q)&&(t[j]<r[i]); j++)
				printf("%d\n",min(max(min(max(a[j]+s,L),R)+ty*(t[j]-r[i-1]),0),x));
			L=min(max(L+ty*(r[i]-r[i-1]),0),x);
			R=min(max(R+ty*(r[i]-r[i-1]),0),x);
			s+=ty*(r[i]-r[i-1]);
		}
}

int main()
{
	work();
	return 0;
}
