Milk Exchange

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?

The first line contains $N$.

The next line contains integers $a\_1,a\_2,...,a\_N$.

Output $N$ lines, where the $i$-th line is the total milk left among all cows after $i$ minutes.