Growing Charges

Medium

A customer has two accounts holding first and second coins. A subscription charges them every day, and the charge grows: on day i (days start at 1) it takes i coins. The money is always taken from the account that currently holds more; on a tie, from the first one. If that account has fewer than i coins, the charge fails and the subscription stops. Return [day, rest1, rest2]: the day on which the charge failed and the balances of the first and second accounts at that moment.

Example 1

first=3, second=1 → [3, 0, 1]

Day 1: 1 is taken from account 1 (2 left). Day 2: account 1 is still larger, 2 is taken (0 left). Day 3: account 2 is larger but holds only 1 < 3, so the charge fails.

Example 2

first=0, second=0 → [1, 0, 0]

On day 1 there is nothing to cover a charge of 1.

Example 3

first=5, second=9 → [5, 1, 3]

Constraints

0 ≤ first, second ≤ 2³¹ − 1

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Topics

Math Simulation

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Input

first=3, second=1

Expected

[3, 0, 1]

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