Codeforces Round #398(Div. 2)D. Cartons of milk

D. Cartons of milk

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Olya likes milk very much. She drinks k cartons of milk each day if she has at least k and drinks all of them if she doesn't. But there's an issue — expiration dates. Each carton has a date after which you can't drink it (you still can drink it exactly at the date written on the carton). Due to this, if Olya's fridge contains a carton past its expiry date, she throws it away.

Olya hates throwing out cartons, so when she drinks a carton, she chooses the one which expires the fastest. It's easy to understand that this strategy minimizes the amount of cartons thrown out and lets her avoid it if it's even possible.

Milk. Best before: 20.02.2017.

The main issue Olya has is the one of buying new cartons. Currently, there are n cartons of milk in Olya's fridge, for each one an expiration date is known (how soon does it expire, measured in days). In the shop that Olya visited there are m cartons, and the expiration date is known for each of those cartons as well.

Find the maximum number of cartons Olya can buy so that she wouldn't have to throw away any cartons. Assume that Olya drank no cartons today.

Input

In the first line there are three integers n, m, k (1 ≤ n, m ≤ 106, 1 ≤ k ≤ n + m) — the amount of cartons in Olya's fridge, the amount of cartons in the shop and the number of cartons Olya drinks each day.

In the second line there are n integers f1, f2, ..., fn (0 ≤ fi ≤ 107) — expiration dates of the cartons in Olya's fridge. The expiration date is expressed by the number of days the drinking of this carton can be delayed. For example, a 0 expiration date means it must be drunk today, 1 — no later than tomorrow, etc.

In the third line there are m integers s1, s2, ..., sm (0 ≤ si ≤ 107) — expiration dates of the cartons in the shop in a similar format.

Output

If there's no way for Olya to drink the cartons she already has in her fridge, print -1.

Otherwise, in the first line print the maximum number x of cartons which Olya can buy so that she wouldn't have to throw a carton away. The next line should contain exactly x integers — the numbers of the cartons that should be bought (cartons are numbered in an order in which they are written in the input, starting with 1). Numbers should not repeat, but can be in arbitrary order. If there are multiple correct answers, print any of them.

Examples

input

3 6 2
1 0 1
2 0 2 0 0 2

output

3
1 2 3

input

3 1 2
0 0 0
1

output

-1

input

2 1 2
0 1
0

output

1
1 

Note

In the first example k = 2 and Olya has three cartons with expiry dates 0, 1 and 1 (they expire today, tomorrow and tomorrow), and the shop has 3 cartons with expiry date 0 and 3 cartons with expiry date 2. Olya can buy three cartons, for example, one with the expiry date 0 and two with expiry date 2.

In the second example all three cartons Olya owns expire today and it means she would have to throw packets away regardless of whether she buys an extra one or not.

In the third example Olya would drink k = 2 cartons today (one she alreay has in her fridge and one from the shop) and the remaining one tomorrow.

题意：家里有n瓶牛奶，超市有m瓶牛奶，主人每天喝k瓶，牛奶有保质期，问在不浪费的情况下，最多能买几瓶牛奶，家里的n瓶牛奶若有浪费输出-1.

思路：很明显贪心的方案是这样的，家里的牛奶保质期越短越早喝越好，超市的牛奶保质期越长，买它越好，家里的牛奶能不能喝完排下序就出答案了，然后就是超市的牛奶买几瓶最好，这里我们二分答案判断就好了，判断的时候不能把两个数组合并然后排序，这样每次判断都要排序会超时的，这里用点技巧就不用排序了，下面给代码：

#include<cstdio>  
#include<algorithm>  
#include<cstring>  
#include<iostream>  
#include<cmath>  
#include<queue>  
#include<functional>  
typedef long long LL;
using namespace std;
#define maxn 1000005
#define ll l,mid,now<<1  
#define rr mid+1,r,now<<1|1  
#define lson l1,mid,l2,r2,now<<1  
#define rson mid+1,r1,l2,r2,now<<1|1  
#define inf 0x3f3f3f3f  
const int mod = 1e9 + 7;
int a[maxn];
int n, m, k;
struct node{
	int value, id;
}b[maxn];
bool check(int num){
	int now1 = 0, now2 = 0;
	while (now1 + now2<n + num){
		if (now1 < n){
			if (now2 < num){
				if (a[now1] < b[num-now2-1].value){
					if ((now1 + now2) / k > a[now1])
						return false;
					else
						now1++;
				}
				else{
					if ((now1 + now2) / k > b[num-now2-1].value)
						return false;
					else
						now2++;
				}
			}
			else{
				if ((now1 + now2) / k > a[now1])
					return false;
				else
					now1++;
			}
		}
		else{
			if ((now1 + now2) / k > b[num-now2-1].value)
				return false;
			else
				now2++;
		}
	}
	return true;
}
bool cmp(node x, node y){
	return x.value > y.value;
}
int main(){
	scanf("%d%d%d", &n, &m, &k);
	for (int i = 0; i < n; i++){
		scanf("%d", &a[i]);
	}
	for (int i = 0; i < m; i++){
		scanf("%d", &b[i].value);
		b[i].id = i + 1;
	}
	sort(a, a + n);
	bool jud = true;
	for (int i = 0; i < n; i++){
		if (i / k>a[i]){
			jud = false;
			break;
		}
	}
	if (jud){
		sort(b, b + m, cmp);
		int l = 1, r = m;
		int ans = 0;
		while (l <= r){
			int mid = l + r >> 1;
			if (check(mid)){
				l = mid + 1;
				ans = mid;
			}
			else{
				r = mid - 1;
			}
		}
		printf("%d\n", ans);
		if (ans)
			printf("%d", b[0].id);
		for (int i = 1; i < ans; i++){
			printf(" %d", b[i].id);
		}
		printf("\n");
	}
	else
		printf("-1\n");
}