187_D. BRT Contract _10254
In the last war of PMP, he defeated all his opponents and advanced to the final round. But after the end of semi-final round evil attacked him from behind and killed him! God bless him. 

Before his death, PMP signed a contract with the bus rapid transit (BRT) that improves public transportations by optimizing time of travel estimation. You should help PMP finish his last contract.

Each BRT line is straight line that passes n intersecting on its ways. At each intersection there is traffic light that periodically cycles between green and red. It starts illuminating green at time zero. During the green phase which lasts for g seconds, traffic is allowed to proceed. After the green phase the light changes to red and remains in this color for r seconds. During the red phase traffic is prohibited from proceeding. If a vehicle reaches the intersection exactly at a time when the light changes to red, it should stop, but the vehicle is clear to proceed if the light has just changed to green.

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All traffic lights have the same timing and are synchronized. In other words the period of red (and green) phase is the same for all of traffic lights and they all start illuminating green at time zero.

The BRT Company has calculated the time that a bus requires to pass each road segment. A road segment is the distance between two consecutive traffic lights or between a traffic light and source (or destination) station. More precisely BRT specialists provide n + 1 positive integers li, the time in seconds that a bus needs to traverse i-th road segment in the path from source to destination. The l1 value denotes the time that a bus needs to pass the distance between source and the first intersection. The ln + 1 value denotes the time between the last intersection and destination.

In one day q buses leave the source station. The i-th bus starts from source at time ti (in seconds). Decision makers of BRT Company want to know what time a bus gets to destination?

The bus is considered as point. A bus will always move if it can. The buses do not interfere with each other. 

Input

The first line of input contains three space-separated positive integers n, g, r (1 ≤ n ≤ 105, 2 ≤ g + r ≤ 109) — the number of intersections, duration of green phase and duration of red phase. Next line contains n + 1 integers li (1 ≤ li ≤ 109) — the time to pass the i-th road segment in the path from source to destination. 

Next line contains a single integer q (1 ≤ q ≤ 105) — the number of buses in a day. The i-th of next q lines contains a single integer ti (1 ≤ ti ≤ 109) — the time when i-th bus leaves the source station.

Output

In the i-th line of output you should print a single integer — the time that i-th bus gets to destination.

Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.

Examples

Input

1 3 2
5 2
5
1
2
3
4
5


Output

8
9
12
12
12


Input

5 3 7
10 1 1 8 900000005 1000000000
3
1
10
1000000000


Output

1900000040
1900000040
2900000030

Note

In the first sample, buses #1, #2 and #5 will reach the destination without waiting behind the red light. But buses #3 and #4 should wait.

In the second sample, first bus should wait at third, fourth and fifth intersections. Second and third buses should wait only at the fifth intersection.
#include <bits/stdc++.h>
using namespace std;
map<int, int> a;
int n, G, S, Q, L, R, j;
map<int, int>::iterator k;
long long d[100005], t[100005];
void ins(int i, int L, int R) {
  if (L == R) return;
  map<int, int>::iterator j = a.lower_bound(L), k = a.upper_bound(R);
  int tmp = (--k)->second;
  a.erase(j, ++k);
  a[L] = i;
  a[R] = tmp;
}
int main() {
  scanf("%d%d%d", &n, &G, &S), S += G, a[0] = n + 1;
  for (int i = 1; i <= n + 1; i++) scanf("%I64d", &d[i]), d[i] += d[i - 1];
  for (int i = n; i; i--) {
    L = (G - d[i]) % S, R = (S - d[i]) % S, L < 0 ? L += S : 0,
    R < 0 ? R += S : 0;
    k = a.upper_bound((S - d[i] % S) % S), j = (--k)->second;
    if (j > n)
      t[i] = d[n + 1] - d[i];
    else
      t[i] = (d[j] - d[i] - 1) / S * S + S + t[j];
    if (L < R)
      ins(i, L, R);
    else
      ins(i, 0, R), ins(i, L, S);
  }
  scanf("%d", &Q);
  while (Q--)
    scanf("%d", &R),
        k = a.upper_bound(R % S), j = (--k)->second,
        printf("%I64d\n",
               j > n ? R + d[n + 1] : (R + d[j] - 1) / S * S + S + t[j]);
  return 0;
}

1 3 2
5 2
5
1
2
3
4
5
 5 3 7
10 1 1 8 900000005 1000000000
3
1
10
1000000000
 5 3 3
24 29 19 27 13 18
3
2
17
15
 5 2 3
19 42 23 36 49 18
3
34
24
20
 5 20 3
45 43 50 40 4 19
3
42
41
26
 5 3 3
24 29 19 27 13 18
3
1
17
15
 5 2 3
19 66 23 36 49 18
3
34
24
20
 5 6 3
45 43 50 40 4 19
3
42
41
26
 1 3 2
5 2
5
1
2
3
4
3
 5 3 3
24 29 19 27 24 18
3
1
17
15
 5 2 3
19 66 23 36 49 19
3
34
24
20
 5 6 3
45 43 50 40 4 19
3
42
69
26
 2 3 2
5 2
5
1
2
3
4
3
 5 3 3
24 29 19 27 24 18
3
1
12
15
 5 2 3
19 66 23 45 49 19
3
34
24
20
 5 6 3
45 7 50 40 4 19
3
42
69
26
 5 3 6
24 29 19 27 24 18
3
1
12
15
 5 2 3
19 90 23 45 49 19
3
34
24
20
 5 6 3
45 12 50 40 4 19
3
42
69
26
 5 2 3
19 90 23 45 41 19
3
34
24
20
 5 6 1
45 12 50 40 4 19
3
42
69
26
 5 3 6
24 53 19 27 25 18
3
1
12
15
 5 6 1
45 12 50 40 4 24
3
42
69
26
 5 3 6
24 53 19 27 25 18
3
1
16
15
 5 6 1
45 15 50 40 4 24
3
42
69
26
 5 5 6
24 53 19 27 25 18
3
1
16
15
 5 5 6
24 53 19 27 25 34
3
1
16
15
 5 5 4
24 53 19 27 25 34
3
1
16
15
 5 5 4
24 53 28 27 25 34
3
1
16
15
 5 5 4
24 53 28 31 25 34
3
1
16
15
 5 5 4
24 53 27 31 25 34
3
1
16
15
 5 5 4
24 53 27 31 25 48
3
1
16
15
 5 3 3
24 29 19 27 13 18
3
2
24
15
 5 2 3
19 32 23 36 49 18
3
34
24
20
 5 20 1
45 43 50 40 4 19
3
42
41
26
 5 3 7
10 1 1 8 900000005 1000000000
3
2
10
1000000000
 5 3 3
24 29 19 27 19 18
3
1
17
15
 5 2 3
19 66 23 36 49 18
3
34
24
36
 5 6 3
45 43 50 40 4 19
3
42
2
26
 1 3 2
5 1
5
1
2
3
4
3
 5 5 3
24 29 19 27 24 18
3
1
17
15
 5 2 3
19 94 23 36 49 19
3
34
24
20
 5 6 3
45 43 40 40 4 19
3
42
69
26
 1 3 2
6 2
5
1
2
3
4
3
 5 2 3
19 66 23 45 49 19
3
41
24
20
 5 6 3
45 7 50 40 1 19
3
42
69
26
 5 2 3
8 90 23 45 49 19
3
34
24
20
 5 3 6
24 29 19 27 25 18
3
1
12
15

8
9
12
12
12
 1900000040
1900000040
2900000030
 133
151
151
 228
218
213
 243
242
230
 133
151
151
 248
238
233
 248
244
230
 8
9
12
12
12
 144
162
162
 249
239
234
 248
275
230
 15
 144
156
162
 259
249
244
 212
239
194
 153
162
171
 284
274
269
 217
244
199
 275
265
260
 212
240
198
 171
180
189
 217
245
203
 171
189
189
 220
248
204
 175
197
197
 191
213
213
 187
198
197
 196
207
206
 205
214
214
 198
214
214
 212
228
228
 133
157
151
 218
208
203
 243
242
227
 1900000040
1900000040
2900000030
 139
157
157
 248
238
248
 248
203
230
 7
8
11
11
11
 146
162
162
 279
269
264
 239
266
221
 9
12
12
12
12
 264
249
244
 209
236
191
 274
264
259
 153
162
171
