Gas Station

There are n gas stations along a circular route, where the amount of gas at the ith station is gas[i].

You have a car with an unlimited gas tank and it costs cost[i] of gas to travel from the ith station to its next (i + 1)th station. You begin the journey with an empty tank at one of the gas stations.

Given two integer arrays gas and cost, return the starting gas station's index if you can travel around the circuit once in the clockwise direction, otherwise return -1. If there exists a solution, it is guaranteed to be unique.

Examples

Input: gas = [1,2,3,4,5], cost = [3,4,5,1,2]

Output: 3

Start at station 3 (index 3). Gas left: 4 - 1 + 5 - 2 + 1 - 3 + 2 - 4 + 3 - 5 = 0.

Constraints

• n == gas.length == cost.length
• 1 <= n <= 10^5
• 0 <= gas[i], cost[i] <= 10^4

Complexity Analysis

Time

O(N)

one pass through the arrays.

Space

O(1)

variables only.

Test Cases

#1 Possible to complete circuit

Input: gas = [1,2,3,4,5], cost = [3,4,5,1,2]

Expected: 3

#2 Total gas is less than total cost

Input: gas = [2,3,4], cost = [3,4,3]

Expected: -1