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>
#define pb push_back
#define mp make_pair
#define X first 
#define Y second
using namespace std;
typedef pair<int, int> pii;
const int N = 222222;
vector<pii> a;
int x, n, ac[N], res[N], q;
int main() {
	scanf("%d", &x);
	scanf("%d", &n);
	for (int i = 1; i <= n; ++i) {
		int t;
		scanf("%d", &t);
		a.pb(mp(t, -1));
	}
	scanf("%d", &q);
	for (int i = 1; i <= q; ++i) {
		int t;
		scanf("%d%d", &t, &ac[i]);
		a.pb(mp(t, i));
	}
	sort(a.begin(), a.end());
	int i = 0, j = x, yi = 0, yj = x, dir = 0, t0 = 0;
	for (int _ = 0; _ < a.size(); ++_) {
		int t = a[_].X;
		if (t != t0) {
			int dt = t - t0;
			if (dir == 0) {
				if (yi >= dt) {
					yi -= dt;
					yj -= dt;
				} else if (yj < dt) {
					yj = yi = 0;
					i = j = 0;
				} else {
					i += dt - yi;
					yi = 0;
					yj -= dt;
				}
			} else {
				if (yj + dt <= x) {
					yi += dt;
					yj += dt;
				} else if (yi + dt > x) {
					i = j = 0;
					yi = yj = x;
				} else {
					j -= yj + dt - x;
					yi += dt;
					yj = x;
				}
			}
		}
		t0 = t;
		int id = a[_].Y;
		if (~id) {
			if (ac[id] <= i) res[id] = yi;
			else if (ac[id] >= j) res[id] = yj;
			else res[id] = yi + ac[id] - i;
		}
		else dir ^= 1;
	}
	for (int i = 1; i <= q; ++i) printf("%d\n", res[i]);
	return 0;
} 