Make Bricks

Background

Congcong is playing a building block game.

Problem Description

We want to make a row of bricks that is $goal$ inches long. We have a number of small bricks ($1$ inch each) and big bricks ($5$ inches each). Return true if it is possible to make the $goal$ by choosing from the given bricks. This is a little harder than it looks and can be done without any loops.

Input Format

Input is given from standard input in the following format.

small big goal

Output Format

Output is printed to standard output in the following format.

result

Sample

3 1 8

true

3 1 9

false

3 2 10

true

Sample Explanation

Sample 1: small = 3, big = 1, goal = 8. We can use $1$ big brick ($5$ inches) and $3$ small bricks ($3$ inches), totaling $5+3=8$ inches. So, return true.

Sample 2: small = 3, big = 1, goal = 9. Even using all bricks, the maximum length is $1 \times 5 + 3 \times 1 = 8$ inches, which cannot reach $9$ inches. So, return false.

Sample 3: small = 3, big = 2, goal = 10. We can use $2$ big bricks ($10$ inches) and $0$ small bricks, totaling $10$ inches. So, return true.

Constraints

Time limit $1$s, Memory limit $1024$ KiB for each test case.