When Will You Save a Million?

You landed your dream job. They pay in geometric progression. In your first month of work, you will get your first paycheck first_month. For every month after, your paycheck will be multiplier times bigger than the previous paycheck.

Create a function that takes the first_month's paycheck and the multiplier and returns the number of months it took for you to save up more than one million. The problem assumes you save 100% of every paycheck.

Examples

million_in_month(10, 2) ➞ 17

million_in_month(100, 1.01) ➞ 464

million_in_month(50, 100) ➞ 4
# Month 1 = 50 (paycheck 50)
# Month 2 = 5050 (paycheck 5,000 + 50 already saved)
# Month 3 = 505050 (paycheck 500,000 + 5,050 already saved)
# Month 4 = 50505050 (paycheck 50,000,000 + 505,050 already saved)

Notes

• Don't forget to return the result in the number of months.
• Return when your savings are greater than 1,000,000.