Farmer John has just given the cows a program to play with! The program contains two integer variables, *x* and *y*, and performs the following operations on a sequence *a*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">2</sub>, ..., *a*<sub class="lower-index">*n*</sub> of positive integers:
 1.  Initially, *x* = 1 and *y* = 0. If, after any step, *x* ≤ 0 or *x* &gt; *n*, the program immediately terminates. 1.  The program increases both *x* and *y* by a value equal to *a*<sub class="lower-index">*x*</sub> simultaneously. 1.  The program now increases *y* by *a*<sub class="lower-index">*x*</sub> while decreasing *x* by *a*<sub class="lower-index">*x*</sub>. 1.  The program executes steps 2 and 3 (first step 2, then step 3) repeatedly until it terminates (it may never terminate). So, the sequence of executed steps may start with: step 2, step 3, step 2, step 3, step 2 and so on. 
The cows are not very good at arithmetic though, and they want to see how the program works. Please help them!

You are given the sequence *a*<sub class="lower-index">2</sub>, *a*<sub class="lower-index">3</sub>, ..., *a*<sub class="lower-index">*n*</sub>. Suppose for each *i* (1 ≤ *i* ≤ *n* - 1) we run the program on the sequence *i*, *a*<sub class="lower-index">2</sub>, *a*<sub class="lower-index">3</sub>, ..., *a*<sub class="lower-index">*n*</sub>. For each such run output the final value of *y* if the program terminates or -1 if it does not terminate.
The first line contains a single integer, *n* (2 ≤ *n* ≤ 2·10<sup class="upper-index">5</sup>). The next line contains *n* - 1 space separated integers, *a*<sub class="lower-index">2</sub>, *a*<sub class="lower-index">3</sub>, ..., *a*<sub class="lower-index">*n*</sub> (1 ≤ *a*<sub class="lower-index">*i*</sub> ≤ 10<sup class="upper-index">9</sup>).
import sys
sys.setrecursionlimit(int(1e6))
n = int(input())
a = [0] * 2 + list(map(int, input().split())) 
vis = [[0] * 2 for x in range(n + 1)] 
dp = [[0] * 2 for x in range(n + 1)]

def dfs(u, s):
	vis[u][s] = 1
	if s == 0:
		v = u + a[u]
	else:
		v = u - a[u]
	if v <= 0 or v > n:
		dp[u][s] = a[u]
	else:
		if v == 1:
			dp[u][s] = -1
		elif vis[v][1 - s] == 1:
			dp[u][s] = -1
		elif vis[v][1 - s] == 2:
			dp[u][s] = a[u] + dp[v][1 - s]
		else:
			dfs(v, 1 - s)
			dp[u][s] = a[u] + dp[v][1 - s]
	vis[u][s] = 2

for i in range(2, n + 1):	
	for j in range(2):
		if not vis[i][j]:
			dfs(i, j)
for i in range(1, n):
	print ((dp[i + 1][1] + i) if dp[i + 1][1] != -1 else -1)
