TASK

Problem

#56

Given integers `a` and `b` in the equation `a*x = b`, print `infinite` if every `x` is a solution, `none` if there are no solutions, and `one` otherwise.

EXAMPLE

Example

Input

0 0

Output

infinite

LIMITS

Constraints

|a|, |b| ≤ 10^9.

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LEARN Theory for this problem

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An `if` / `else if` / `else` chain checks alternatives from top to bottom. Put more specific or higher-priority conditions first.

Connection to “Number of Solutions for ax=b”: here, branching selects a case using a Boolean condition; test order matters when cases overlap.

💡

NEED HELP? Hints

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['List the possible cases and make them mutually exclusive.', 'After solving “Number of Solutions for ax=b”, verify the algorithm on your own small example and on an allowed boundary case. Print only the required result with no extra text.']

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ANSWER Solution

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#include <iostream>
#include <algorithm>
using namespace std;
int main() {
    long long a, b;
    cin >> a >> b;
    if (a == 0 && b == 0) cout << "infinite";
    else if (a == 0) cout << "none";
    else cout << "one";
    cout << '\n';
    return 0;
}