Hybrid Sequence Generation

Given two initial integers a and b, generate a sequence of n terms defined as follows:

Let the sequence be \(s_0, s_1, s_2, \dots, s_{n-1}\) with \(s_0 = a\) and \(s_1 = b\). For every index \(i \ge 2\), the term \(s_i\) is determined by:

• If \(i\) is even, then \(s_i = s_{i-2} + s_{i-1}\). That is, \(s_i = s_{i-2} + s_{i-1}\).
• If \(i\) is odd, then \(s_i = s_{i-2} \times s_{i-1}\). That is, \(s_i = s_{i-2} \times s_{i-1}\).

Your task is to generate the first n terms of this hybrid sequence and output them as space-separated values on one line.

Examples:

Input: 2 3 5
Output: 2 3 5 15 20
Input: 1 1 8
Output: 1 1 2 2 4 8 12 96

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inputFormat

The input consists of a single line containing three space-separated integers a, b, and n:

• a - the first term of the sequence.
• b - the second term of the sequence.
• n - the number of terms to generate.

Constraints: All values are positive integers.

outputFormat

Output a single line containing n space-separated integers, which are the first n terms of the hybrid sequence.

## sample

2 3 5

2 3 5 15 20