Description

Scientists have discovered a unique species of insect in tropical forests with remarkable reproductive abilities. Each pair of adult insects produces y pairs of eggs every x months, and each pair of eggs takes two months to mature into adults. Assuming no adult dies, starting with only one pair of adults in the first month, and adults do not lay eggs in the first month after maturing (they start laying eggs after x months), how many pairs of adults will there be after z months? The constraints are: 0 ≤ x ≤ 20, 1 ≤ y ≤ 20, x ≤ z ≤ 50.

Input Format

The values of x, y, z.

Output Format

The number of adult pairs after z months.

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