Dreamoon Likes Coloring

Dreamoon likes coloring cells very much.

There is a row of n cells. Initially, all cells are empty (don’t contain any color). Cells are numbered from 1 to n.

You are given an integer m and m integers l1,l2,…,lm (1≤li≤n)

Dreamoon will perform m operations.

In i-th operation, Dreamoon will choose a number pi from range [1,n−li+1] (inclusive) and will paint all cells from pi to pi+li−1 (inclusive) in i-th color. Note that cells may be colored more one than once, in this case, cell will have the color from the latest operation.

Dreamoon hopes that after these m operations, all colors will appear at least once and all cells will be colored. Please help Dreamoon to choose pi in each operation to satisfy all constraints.

Input
The first line contains two integers n,m (1≤m≤n≤100000).

The second line contains m integers l1,l2,…,lm (1≤li≤n).

Output
If it’s impossible to perform m operations to satisfy all constraints, print “’-1” (without quotes).

Otherwise, print m integers p1,p2,…,pm (1≤pi≤n−li+1), after these m operations, all colors should appear at least once and all cells should be colored.

If there are several possible solutions, you can print any.

Examples

input
5 3
3 2 2
output
2 4 1
input
10 1
1
output
-1

#include <bits/stdc++.h>#define ll long long
using namespace std;
const int N = 1e5 + 10;
int ans[N], l[N], n, m;
ll sum;int main() {cin >> n >> m;for (int i = 1; i <= m; i++)scanf("%d", &l[i]), sum += l[i];if (sum < n) {puts("-1");return 0;}for (int i = 1; i <= m; i++)if (n - l[i] + 1 < i) {puts("-1");return 0;}ll rec = sum - n;int now = 1;for (int i = 1; i <= m; i++) {ans[i] = now;int res = min(rec, 1ll * l[i] - 1);rec -= res;now = now + l[i] - res;}for (int i = 1; i <= m; i++)printf("%d ", ans[i]);return 0;
}

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