Problem:
Score : 600 points

Problem Statement

Given is an integer sequence of length N+1: A_0, A_1, A_2, \ldots, A_N. Is there a binary tree of depth N such that, for each d = 0, 1, \ldots, N, there are exactly A_d leaves at depth d? If such a tree exists, print the maximum possible number of vertices in such a tree; otherwise, print -1.

Notes

A binary tree is a rooted tree such that each vertex has at most two direct children.

A leaf in a binary tree is a vertex with zero children.

The depth of a vertex v in a binary tree is the distance from the tree's root to v. (The root has the depth of 0.)

The depth of a binary tree is the maximum depth of a vertex in the tree.

Constraints

0 \leq N \leq 10^5

0 \leq A_i \leq 10^{8} (0 \leq i \leq N)

A_N \geq 1

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_0 A_1 A_2 \cdots A_N

Output

Print the answer as an integer.

Sample Input 1

3
0 1 1 2

Sample Output 1

7

Below is the tree with the maximum possible number of vertices. It has seven vertices, so we should print 7.

Sample Input 2

4
0 0 1 0 2

Sample Output 2

10

Sample Input 3

2
0 3 1

Sample Output 3

-1

Sample Input 4

1
1 1

Sample Output 4

-1

Sample Input 5

10
0 0 1 1 2 3 5 8 13 21 34

Sample Output 5

264

Solution in Go (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"container/heap"
	"fmt"
	"math"
	"os"
	"strconv"
)

const (
	initialBufSize = 10000
	maxBufSize     = 1000000
	mod            = 1e9 + 7
)

var (
	sc *bufio.Scanner = func() *bufio.Scanner {
		sc := bufio.NewScanner(os.Stdin)
		buf := make([]byte, initialBufSize)
		sc.Buffer(buf, maxBufSize)
		sc.Split(bufio.ScanWords)
		return sc
	}()
)

func main() {
	N := getInt()
	A := getIntArray(N+1)

	if N == 0 {
		if A[0] == 1 {
			fmt.Println(1)
		} else {
			fmt.Println(-1)
		}
		return
	}

	total := 0
	for _, a := range A {
		total += a
	}

	result := 1
	rest := 1
	for i := 1; i <= N; i++ {
		//fmt.Println("Before: ", result, rest, total)

		num := 0
		if 2 * rest <= total {
			num = 2 * rest
		} else {
			num = total
		}

		result += num
		rest = num - A[i]
		total -= A[i]

		//fmt.Println("After: ", result, rest, total)

		if rest < 0 {
			result = -1
			break
		}
	}

	fmt.Println(result)
}

type Graph struct {
	n     int
	edges []map[int]struct{}
}

func NewGraph(n int) *Graph {
	g := &Graph{
		n:     n,
		edges: make([]map[int]struct{}, n),
	}
	for i := 0; i < n; i++ {
		g.edges[i] = make(map[int]struct{})
	}
	return g
}

func (g *Graph) AddEdge(u, v int) {
	g.edges[v][u] = struct{}{}
	g.edges[u][v] = struct{}{}
}

func dfs(c int, edges []map[int]struct{}, visited map[int]struct{}) {
	visited[c] = struct{}{}

	for v := range edges[c] {
		_, flag := visited[v]
		if flag {
			continue
		}
		dfs(v, edges, visited)
	}
}

func bfs(c int, graph *Graph) {
	standby := make(map[int]struct{})
	next := make([]int, 0)
	next = append(next, c)
	visited := make(map[int]struct{})

	for ; len(next) != 0; {
		u := next[0]
		next = next[1:]
		visited[u] = struct{}{}
		delete(standby, u)

		for v := range graph.edges[u] {
			_, flag := visited[v]
			if flag {
				continue
			}

			// なにか処理

			if _, exists := standby[v]; !exists {
				next = append(next, v)
				standby[v] = struct{}{}
			}
		}
	}
}

func getInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func getIntArray(n int) []int {
	array := make([]int, n)
	for i := 0; i < n; i++ {
		array[i] = getInt()
	}
	return array
}

func getString() string {
	sc.Scan()
	return sc.Text()
}

func getStringArray(n int) []string {
	array := make([]string, n)
	for i := 0; i < n; i++ {
		array[i] = getString()
	}
	return array
}

func abs(a int) int {
	return int(math.Abs(float64(a)))
}

func pow(p, q int) int {
	return int(math.Pow(float64(p), float64(q)))
}

func powMod(n, p int) int {
	if p == 0 {
		return 1
	} else if p%2 == 0 {
		t := powMod(n, p/2)
		return calcMod(t * t)
	} else {
		return calcMod(n * powMod(n, p-1))
	}
}

func min(nums ...int) int {
	if len(nums) == 0 {
		panic("funciton min() requires at least one argument.")
	}
	res := nums[0]
	for i := 0; i < len(nums); i++ {
		res = int(math.Min(float64(res), float64(nums[i])))
	}
	return res
}

func max(nums ...int) int {
	if len(nums) == 0 {
		panic("funciton max() requires at least one argument.")
	}
	res := nums[0]
	for i := 0; i < len(nums); i++ {
		res = int(math.Max(float64(res), float64(nums[i])))
	}
	return res
}

func strSearch(a []string, b string) bool {
	for i := 0; i < len(a); i++ {
		if a[i] == b {
			return true
		}
	}
	return false
}

func printIntArray(array []int) {
	strArray := fmt.Sprint(array)
	fmt.Println(strArray[1 : len(strArray)-1])
}

func calcMod(x int) int {
	return x % mod
}

func reverse(s string) string {
	runes := []rune(s)
	for i, j := 0, len(runes)-1; i < j; i, j = i+1, j-1 {
		runes[i], runes[j] = runes[j], runes[i]
	}
	return string(runes)
}

func isPrime(n int) bool {
	if n < 2 {
		return false
	} else if n == 2 {
		return true
	} else if n % 2 == 0 {
		return false
	}

	sqrtN := int(math.Sqrt(float64(n)))
	for i := 3; i <= sqrtN; i += 2 {
		if n % i == 0 {
			return false
		}
	}

	return true
}

func contains(s []int, e int) bool {
	for _, v := range s {
		if e == v {
			return true
		}
	}
	return false
}

func makeRange(min, max int) []int {
	a := make([]int, max-min+1)
	for i := range a {
		a[i] = min + i
	}
	return a
}

func powerset2(nums []int) [][]int {
	length := int(math.Pow(2, float64(len(nums))))
	result := make([][]int, length)

	index := 0
	result[index] = []int{}
	index++

	for _, n := range nums {
		max := index
		for i := 0; i < max; i++ {
			result[index] = copyAndAppend(result[i], n)
			index++
		}
	}

	return result
}

func copyAndAppend(nums []int, n int) []int {
	dst := make([]int, len(nums)+1)
	copy(dst, nums)
	dst[len(nums)] = n
	return dst
}

func calcGcd(x, y int) int {
	if y == 0 {
		return x
	} else if x >= y {
		return calcGcd(y, x % y)
	} else {
		return calcGcd(x, y % x)
	}
}

func getDivisor(n int) []int {
	divisor := make(map[int]struct{})
	divisor[1] = struct{}{}
	if n != 1 {
		divisor[n] = struct{}{}
	}

	sqrt := int(math.Sqrt(float64(n)))
	for i := 2; i <= sqrt; i++ {
		if n % i == 0 {
			divisor[i] = struct{}{}
			divisor[n/i] = struct{}{}
		}
	}

	var divisorArray []int
	for d := range divisor {
		divisorArray = append(divisorArray, d)
	}
	return divisorArray
}

type intHeap []int

func (h intHeap) Len() int {
	return len(h)
}

func (h intHeap) Less(i, j int) bool {
	return h[i] > h[j]
}

func (h intHeap) Swap(i, j int) {
	h[i], h[j] = h[j], h[i]
}

func (h *intHeap) Push(x interface{}) {
	*h = append(*h, x.(int))
}

func (h *intHeap) Pop() interface{} {
	old := *h
	n := len(old)
	x := old[n-1]
	*h = old[0 : n-1]
	return x
}

func initHeap() *intHeap {
	ih := &intHeap{}
	heap.Init(ih)
	return ih
}

func (h *intHeap) pushHeap(n int) {
	heap.Push(h, n)
}

func (h *intHeap) popHeap() int {
	return heap.Pop(h).(int)
}

func factMod(n int) int {
	value := 1
	for ; n > 1; n-- {
		value = calcMod(value * n)
	}
	return value
}

func combinationMod(n, k int) int {
	factN := factMod(n)
	factK := factMod(k)
	factNK := factMod(n - k)
	factKR := powMod(factK, mod - 2)
	factNKR := powMod(factNK, mod - 2)
	return calcMod(factN * calcMod(factKR * factNKR))
}

func primeFactors(n int) [] int {
	factors := make([]int, 0)
	i := 2
	for i * i <= n {
		r := n % i
		if r != 0 {
			i += 1
		} else if r == 0 {
			n /= i
			factors = append(factors, i)
		}
	}
	if n > 1 {
		factors = append(factors, n)
	}
	return factors
}