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>

const int MAXN = 100010;
int qa[MAXN], ansl[MAXN];
std::map<int, std::vector<int> > qry;
int X, Q;
int main() {
	std::ios_base::sync_with_stdio(false), std::cin.tie(0);
	std::cin >> X >> Q;
	for (int i = 1, t; i <= Q; ++i)
		std::cin >> t, qry[t].push_back(-1);
	std::cin >> Q;
	for (int i = 1, t; i <= Q; ++i)
		std::cin >> t >> qa[i], qry[t].push_back(i);
	int lx = 0, ly = 0, rx = X, ry = X, lst = 0, typ = 0;
	for (auto t : qry) {
		int d = t.first - lst; lst = t.first;
		ly -= d, ry -= d;
		if (ly < 0) lx -= ly, ly = 0;
		if (ry < 0) rx += ry, ry = 0;
		if (lx >= rx) lx = rx = 0;
		for (auto i : t.second) {
			if (i == -1) ly = X - ly, ry = X - ry, typ ^= 1;
			else {
				if (qa[i] <= lx) ansl[i] = ly;
				else if (qa[i] >= rx) ansl[i] = ry;
				else ansl[i] = ly + (ry - ly) / (rx - lx) * (qa[i] - lx);
				if (typ) ansl[i] = X - ansl[i];
			}
		}
	}
	for (int i = 1; i <= Q; ++i) std::cout << ansl[i] << '\n';
	return 0;
}
