Discription
You are given two multisets A and B. Each multiset has exactly n integers each between 1 and n inclusive. Multisets may contain multiple copies of the same number.
You would like to find a nonempty subset of A and a nonempty subset of B such that the sum of elements in these subsets are equal. Subsets are also multisets, i.e. they can contain elements with equal values.
If no solution exists, print - 1. Otherwise, print the indices of elements in any such subsets of A and B that have the same sum.
Input
The first line of the input contains a single integer n (1 ≤ n ≤ 1 000 000) — the size of both multisets.
The second line contains n integers, denoting the elements of A. Each element will be between 1 and n inclusive.
The third line contains n integers, denoting the elements of B. Each element will be between 1 and n inclusive.
Output
If there is no solution, print a single integer - 1. Otherwise, your solution should be printed on four lines.
The first line should contain a single integer ka, the size of the corresponding subset of A. The second line should contain ka distinct integers, the indices of the subset of A.
The third line should contain a single integer kb, the size of the corresponding subset of B. The fourth line should contain kb distinct integers, the indices of the subset of B.
Elements in both sets are numbered from 1 to n. If there are multiple possible solutions, print any of them.
Examples
Input
10
10 10 10 10 10 10 10 10 10 10
10 9 8 7 6 5 4 3 2 1
Output
1
2
3
5 8 10
Input
5
4 4 3 3 3
2 2 2 2 5
Output
2
2 3
2
3 5 一道神构造。
设sa[]为a[]的前缀和，sb[]为b的前缀和，对于每个0<=i<=n,我们找到一个最大的使得sb[j]<=sa[i]的j，这样每个sa[i]-sb[j]都是[0,n-1]的整数了(因为如果sa[i]-sb[j]>=n的话，j可以继续后移(a[],b[]中元素都<=n))
所以至少会有一对 i和i'满足 sa[i]-sb[j] == sa[i']-sb[j']，直接输出就行了。。
#include<bits/stdc++.h>
#define ll long long
using namespace std;
const int maxn=1000005;
ll a[maxn],b[maxn];
int px[maxn],py[maxn],n;
inline int read(){
int x=0; char ch=getchar();
for(;!isdigit(ch);ch=getchar());
for(;isdigit(ch);ch=getchar()) x=x*10+ch-'0';
return x;
}
void W(int x){ if(x>=10) W(x/10); putchar(x%10+'0');}
int main(){
n=read();
for(int i=1;i<=n;i++) a[i]=read(),a[i]+=a[i-1];
for(int i=1;i<=n;i++) b[i]=read(),b[i]+=b[i-1];
for(int i=0,j=0,D;i<=n;i++){
for(;j<n&&b[j+1]<=a[i];j++);
D=a[i]-b[j];
if(px[D]){
W(i-px[D]+1),puts("");
for(int o=px[D];o<=i;o++) W(o),putchar(' ');
puts(""),W(j-py[D]+1),puts("");
for(int o=py[D];o<=j;o++) W(o),putchar(' ');
return 0;
}
px[D]=i+1,py[D]=j+1;
}
return 0;
}
