Who Has Seen the Wind

Margaret has watched the wind drift over the prairies for a long time. From these observations she has built a formula that predicts the altitude of a weather balloon launched from her house. Specifically, the altitude $A$ (in metres above the ground) at hour $t$ after the launch is:

$A = -6t^4 + h t^3 + 2t^2 + t$

where $h$ is an integer humidity value between $0$ and $100$ inclusive.

Margaret wants to know the earliest hour (if any) at which the balloon will hit the ground after launch, as long as it is no later than the maximum time $M$ she is willing to wait. The balloon is considered to touch the ground when $A \le 0$.

To find this, compute the altitude at $t = 1$, $t = 2$, $\dots$ until the balloon touches the ground or $t = M$ is reached.

Two non-negative integers are given: $h$, the humidity factor, followed by $M$, the maximum number of hours Margaret will wait for the balloon to return to the ground. You may assume $0 \le h \le 100$ and $0 < M < 240$.

Print exactly one of the following on a single line:

• The balloon does not touch ground in the given time.
• The balloon first touches ground at hour: T

where $T$ is the positive integer representing the earliest hour at which the altitude is less than or equal to zero.