Factory Production Time

All machines start at time 0 and work independently. A machine with time t finishes one item after t seconds, another after 2t seconds, and so on. Find the earliest whole second when their combined production reaches the target.

Implement factory_machines(times, target).

Input

times: Seconds needed for one item on each machine.

target: The number of completed items required.

Output

Return the minimum elapsed seconds.

Constraints

1 ≤ machines ≤ 200,000. Each time and the target are between 1 and 1,000,000,000. The answer fits signed 64-bit.

Examples

Input:
times = [2, 3]
target = 5

Expected output:
expected = 6

Input:
std::vector<long long> times = {2, 3};
long long target = 5;

Expected output:
long long expected = 6;

Input:
long[] times = new long[] {2, 3};
long target = 5;

Expected output:
long expected = 6;

Input:
times = [4]
target = 3

Expected output:
expected = 12

Input:
std::vector<long long> times = {4};
long long target = 3;

Expected output:
long long expected = 12;

Input:
long[] times = new long[] {4};
long target = 3;

Expected output:
long expected = 12;

References

This challenge is adapted for CodeUtility. Follow the statement and constraints above.

• Factory Machines — 1620