Minimum Elevator Rides

Each person must ride exactly once. Any group can share a ride if the sum of its weights is no greater than capacity. People may be regrouped freely; their input order does not matter. Minimize the number of rides.

Implement elevator_rides(weights, capacity).

Input

weights: The weight of each person.

capacity: The maximum combined weight in a ride.

Output

Return the minimum number of rides.

Constraints

1 ≤ people ≤ 20. 1 ≤ capacity ≤ 1,000,000,000. Every weight is between 1 and capacity.

Examples

Input:
weights = [3, 4, 5]
capacity = 7

Expected output:
expected = 2

Input:
std::vector<long long> weights = {3, 4, 5};
long long capacity = 7;

Expected output:
long long expected = 2;

Input:
long[] weights = new long[] {3, 4, 5};
long capacity = 7;

Expected output:
long expected = 2;

Input:
weights = [2, 2, 2]
capacity = 6

Expected output:
expected = 1

Input:
std::vector<long long> weights = {2, 2, 2};
long long capacity = 6;

Expected output:
long long expected = 1;

Input:
long[] weights = new long[] {2, 2, 2};
long capacity = 6;

Expected output:
long expected = 1;

References

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

• Elevator Rides — 1653