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 <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <queue>
#include <ctime>
#include <cassert>
#include <complex>
#include <string>
#include <cstring>
using namespace std;

#ifdef LOCAL
	#define eprintf(...) fprintf(stderr, __VA_ARGS__)
#else
	#define eprintf(...) 42
#endif

typedef long long ll;
typedef pair<int, int> pii;
#define mp make_pair

const int N = 100100;
int n;
int X;
int a[N];

int main()
{
//	freopen("input.txt", "r", stdin);
//	freopen("output.txt", "w", stdout);

	scanf("%d%d", &X, &n);
	n++;
	for (int i = 1; i < n; i++)
		scanf("%d", &a[i]);
	int q;
	scanf("%d", &q);
	int l = 0, r = X;
	int forL = 0;
	int it = 0;
	int z = 0;
	while(q--) {
		int t, w;
		scanf("%d%d", &t, &w);
		while(it + 1 < n && a[it + 1] <= t) {
			if (z == 0) {
				forL -= a[it + 1] - a[it];
			} else {
				forL += a[it + 1] - a[it];
			}
			if (forL < 0) {
				l -= forL;
				forL = 0;
			}
			if (forL + r - l > X) {
				r -= forL + r - l - X;
				forL = X - r + l;
			}
			if (l > r) {
				l = r = 0;
				if (forL > X)
					forL = X;
			}
			z ^= 1;
			it++;
		}
		t -= a[it];
		if (w < l) w = l;
		if (w > r) w = r;
		w = forL + w - l;
		if (z == 0)
			w -= t;
		else
			w += t;
		if (w < 0) w = 0;
		if (w > X) w = X;
		printf("%d\n", w);
	}

	return 0;
}
