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;

multiset<int> ms;
int fl[100005];

int main() {
  int x,n;
  scanf("%d%d",&x,&n);
  for(int i=0;i<n;i++) scanf("%d",fl+i);
  fl[n] = 1e9+7;
  int q,i=0,pt=0,lb=0, lv=0, rb=x, rv=x;
  bool up=false;
  scanf("%d",&q);
  while(q--) {
    int t,a;
    scanf("%d%d",&t,&a);
    while(pt<t) {
      if(fl[i] > t) {
        int v = (up?1:-1)*(t-pt);
        lv += v;
        rv += v;
        pt = t;
      } else {
        int v = (up?1:-1)*(fl[i]-pt);
        up = !up;
        pt = fl[i++];
        lv += v;
        rv += v;
      }
      if(rv > x) {
        rb -= rv-x;
        rv = x;
        if(lv > x) {
          lb = rb;
          lv = x;

        }
      }
      if(lv < 0) {
        lb -= lv;
        lv = 0;
        if(rv < 0) {
          rb = lb;
          rv = 0;
        }
      }
      if(lb<0) lb = 0;
      if(lb>x) lb = x;
      if(rb<0) rb = 0;
      if(rb>x) rb = x;
    }
    if(a <= lb) printf("%d\n",lv);
    else if(a >= rb) printf("%d\n",rv);
    else printf("%d\n",lv + (a-lb));
  }
}
