B. Resource Distributiontime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputOne department of some software company has n servers of different specifications. Servers are indexed with consecutive integers from 1 to n. Suppose that the specifications of the j-th server may be expressed with a single integer number c_j of artificial resource units.In order for production to work, it is needed to deploy two services S_1 and S_2 to process incoming requests using the servers of the department. Processing of incoming requests of service S_i takes x_i resource units.The described situation happens in an advanced company, that is why each service may be deployed using not only one server, but several servers simultaneously. If service S_i is deployed using k_i servers, then the load is divided equally between these servers and each server requires only x_i / k_i (that may be a fractional number) resource units.Each server may be left unused at all, or be used for deploying exactly one of the services (but not for two of them simultaneously). The service should not use more resources than the server provides.Determine if it is possible to deploy both services using the given servers, and if yes, determine which servers should be used for deploying each of the services.InputThe first line contains three integers n, x_1, x_2 (2 \leq n \leq 300\,000, 1 \leq x_1, x_2 \leq 10^9) — the number of servers that the department may use, and resource units requirements for each of the services.The second line contains n space-separated integers c_1, c_2, \ldots, c_n (1 \leq c_i \leq 10^9) — the number of resource units provided by each of the servers.OutputIf it is impossible to deploy both services using the given servers, print the only word "No" (without the quotes).Otherwise print the word "Yes" (without the quotes). In the second line print two integers k_1 and k_2 (1 \leq k_1, k_2 \leq n) — the number of servers used for each of the services.In the third line print k_1 integers, the indices of the servers that will be used for the first service.In the fourth line print k_2 integers, the indices of the servers that will be used for the second service.No index may appear twice among the indices you print in the last two lines. If there are several possible answers, it is allowed to print any of them.ExamplesInput6 8 163 5 2 9 8 7OutputYes3 21 2 65 4Input4 20 3221 11 11 12OutputYes1 312 3 4Input4 11 325 5 16 16OutputNoInput5 12 207 8 4 11 9OutputNoNoteIn the first sample test each of the servers 1, 2 and 6 will will provide 8 / 3 = 2.(6) resource units and each of the servers 5, 4 will provide 16 / 2 = 8 resource units.In the second sample test the first server will provide 20 resource units and each of the remaining servers will provide 32 / 3 = 10.(6) resource units.
Input6 8 163 5 2 9 8 7
OutputYes3 21 2 65 4
['binary search', 'implementation', 'sortings', '*1700']