Farmer John's $N$ $(1 \leq N \leq 5 \cdot 10^5)$ cows are lined up in a circle. The $i$th cow has a bucket with integer capacity $a_i$ $(1 \leq a_i \leq 10^9)$ liters. All buckets are initially full.

Every minute, cow $i$ will pass all the milk in their bucket to cow $i+1$ for $1\le i<N$, with cow $N$ passing its milk to cow $1$. All exchanges happen simultaneously (i.e., if a cow has a full bucket but gives away $x$ liters of milk and also receives $x$ liters, her milk is preserved). If a cow's total milk ever ends up exceeding $a_i$, then the excess milk will be lost.

After each of $1, 2, \dots, N$ minutes, how much total milk is left among all cows?

SAMPLE INPUT:

6
2 2 2 1 2 1

SAMPLE OUTPUT:

8
7
6
6
6
6

• After $1$ minute, the amount of milk in each bucket is $[1, 2, 2, 1, 1, 1]$ so the total amount of milk is $8$.
• After $2$ minutes, the amount of milk in each bucket is $[1, 1, 2, 1, 1, 1]$ so the total amount of milk is $7$.
• After $3$ minutes, the amount of milk in each bucket is $[1, 1, 1, 1, 1, 1]$ so the total amount of milk is $6$.
• After $4$ minutes, the amount of milk in each bucket is $[1, 1, 1, 1, 1, 1]$ so the total amount of milk is $6$.
• After $5$ minutes, the amount of milk in each bucket is $[1, 1, 1, 1, 1, 1]$ so the total amount of milk is $6$.
• After $6$ minutes, the amount of milk in each bucket is $[1, 1, 1, 1, 1, 1]$ so the total amount of milk is $6$.

SAMPLE INPUT:

8
3 8 6 4 8 3 8 1

SAMPLE OUTPUT:

25
20
17
14
12
10
8
8

After $1$ minute, the amount of milk in each bucket is $[1, 3, 6, 4, 4, 3, 3, 1]$ so the total amount of milk is $25$.

SAMPLE INPUT:

10
9 9 10 10 6 8 2 1000000000 1000000000 1000000000

SAMPLE OUTPUT:

2000000053
1000000054
56
49
42
35
28
24
20
20

Problem credits: Chongtian Ma, Alex Liang, Patrick Deng