Codeforces-975C - Valhalla Siege 前缀和 思维

C. Valhalla Siege

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Ivar the Boneless is a great leader. He is trying to capture Kattegat from Lagertha. The war has begun and wave after wave Ivar's warriors are falling in battle.

Ivar has nn warriors, he places them on a straight line in front of the main gate, in a way that the ii-th warrior stands right after (i−1)(i−1)-th warrior. The first warrior leads the attack.

Each attacker can take up to aiai arrows before he falls to the ground, where aiai is the ii-th warrior's strength.

Lagertha orders her warriors to shoot kiki arrows during the ii-th minute, the arrows one by one hit the first still standing warrior. After all Ivar's warriors fall and all the currently flying arrows fly by, Thor smashes his hammer and all Ivar's warriors get their previous strengths back and stand up to fight again. In other words, if all warriors die in minute tt, they will all be standing to fight at the end of minute tt.

The battle will last for qq minutes, after each minute you should tell Ivar what is the number of his standing warriors.

Input

The first line contains two integers nn and qq (1≤n,q≤2000001≤n,q≤200000) — the number of warriors and the number of minutes in the battle.

The second line contains nn integers a1,a2,…,ana1,a2,…,an (1≤ai≤1091≤ai≤109) that represent the warriors' strengths.

The third line contains qq integers k1,k2,…,kqk1,k2,…,kq (1≤ki≤10141≤ki≤1014), the ii-th of them represents Lagertha's order at the ii-th minute: kiki arrows will attack the warriors.

Output

Output qq lines, the ii-th of them is the number of standing warriors after the ii-th minute.

Examples

input

Copy

5 5
1 2 1 2 1
3 10 1 1 1

output

Copy

3
5
4
4
3

input

Copy

4 4
1 2 3 4
9 1 10 6

output

Copy

1
4
4
1

Note

In the first example:

• after the 1-st minute, the 1-st and 2-nd warriors die.
• after the 2-nd minute all warriors die (and all arrows left over are wasted), then they will be revived thus answer is 5 — all warriors are alive.
• after the 3-rd minute, the 1-st warrior dies.
• after the 4-th minute, the 2-nd warrior takes a hit and his strength decreases by 1.
• after the 5-th minute, the 2-nd warrior dies

题意：你有n个士兵，每个士兵的生命值为

aiai，有q轮攻击，每轮攻击的伤害值为kiki，如果在某一轮中士兵全部死光了，那么在这一轮结束的时候就会全部复活，且这一轮攻击剩下的伤害就会被忽略，问你每轮攻击结束后你会有多少个士兵。

题解：对n个士兵的生命值记一下前缀和，每轮攻击的时候用upper_bound找一下前缀和里第一个大于

kiki的值所对应的编号，假设这一轮中upper_bound的结果为cur，那么前cur - 1个士兵一定全部死完了，所以就会剩下n - cur + 1个士兵。

（这里前缀和处理的思想很实用，为了用二分优化时间，我们用前缀和的形式把多次造成的伤害记录为一次，这样使用二分的时候就简单很多了。）

题目：

Ivar the Boneless is a great leader. He is trying to capture Kattegat from Lagertha. The war has begun and wave after wave Ivar’s warriors are falling in battle.

Ivar has nn warriors, he places them on a straight line in front of the main gate, in a way that the ii-th warrior stands right after (i−1)(i−1)-th warrior. The first warrior leads the attack.

Each attacker can take up to aiai arrows before he falls to the ground, where aiai is the ii-th warrior’s strength.

Lagertha orders her warriors to shoot kiki arrows during the ii-th minute, the arrows one by one hit the first still standing warrior. After all Ivar’s warriors fall and all the currently flying arrows fly by, Thor smashes his hammer and all Ivar’s warriors get their previous strengths back and stand up to fight again. In other words, if all warriors die in minute tt, they will all be standing to fight at the end of minute tt.

The battle will last for qq minutes, after each minute you should tell Ivar what is the number of his standing warriors.

Input

The first line contains two integers nn and q(1≤n,q≤200 000)q(1≤n,q≤200 000) — the number of warriors and the number of minutes in the battle.

The second line contains nn integers a1,a2,…,an(1≤ai≤109)a1,a2,…,an(1≤ai≤109) that represent the warriors’ strengths.

The third line contains qq integers k1,k2,…kq(1≤ki≤1014)k1,k2,…kq(1≤ki≤1014), the ii-th of them represents Lagertha’s order at the ii-th minute: kiki arrows will attack the warriors.

Output

Output qq lines, the ii-th of them is the number of standing warriors after the ii-th minute.

Examples

input

5 5
1 2 1 2 1
3 10 1 1 1

• 1
• 2
• 3

output

3
5
4
4
3

• 1
• 2
• 3
• 4
• 5

input

4 4
1 2 3 4
9 1 10 6

• 1
• 2
• 3

output

1
4
4
1

• 1
• 2
• 3
• 4

Note

In the first example:

after the 1-st minute, the 1-st and 2-nd warriors die. 
after the 2-nd minute all warriors die (and all arrows left over are wasted), then they will be revived thus answer is 5 — all warriors are alive. 
after the 3-rd minute, the 1-st warrior dies. 
after the 4-th minute, the 2-nd warrior takes a hit and his strength decreases by 1. 
after the 5-th minute, the 2-nd warrior dies.

---

题意：

  你有n个士兵，每个士兵的生命值为aiai，有q轮攻击，每轮攻击的伤害值为kiki，如果在某一轮中士兵全部死光了，那么在这一轮结束的时候就会全部复活，且这一轮攻击剩下的伤害就会被忽略，问你每轮攻击结束后你会有多少个士兵。

---

思路：

  对n个士兵的生命值记一下前缀和，每轮攻击的时候用upper_bound找一下前缀和里第一个大于kiki的值所对应的编号，假设这一轮中upper_bound的结果为cur，那么前cur - 1个士兵一定全部死完了，所以就会剩下n - cur + 1个士兵。

（用前缀和的思想把多次的伤寒换算为一次，这样使用二分的时候就简单很多了）

ac代码：

#include <cstdio>
#include <iostream>
#include <cstring>
#include <queue>
#include <algorithm>
using namespace std;
typedef long long ll;
const int maxn = int(2e5) + ;
ll a[maxn], k[maxn], sum[maxn], dmg;

int main() {
    int n, q;
    scanf("%d%d", &n, &q);
    for (int i = ; i <= n; i++) scanf("%lld", a + i), sum[i] = sum[i - ] + a[i];
    for (int i = ; i <= q; i++) scanf("%lld", k + i);
    for (int turn = , cur; turn <= q; turn++)
   {
        dmg += k[turn];
        if (dmg >= sum[n]) dmg = , printf("%d\n", n);
        else printf("%d\n", n - int(std::upper_bound(sum + , sum +  + n, dmg) - sum - ));
    }
    return ;
}