One 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.


-----Input-----

The 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.


-----Output-----

If 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.


-----Examples-----
Input
6 8 16
3 5 2 9 8 7

Output
Yes
3 2
1 2 6
5 4
Input
4 20 32
21 11 11 12

Output
Yes
1 3
1
2 3 4

Input
4 11 32
5 5 16 16

Output
No

Input
5 12 20
7 8 4 11 9

Output
No



-----Note-----

In 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.

Source: codeforces | Difficulty: MEDIUM_HARD
Tags: Sorting

Implementation


Solutions:
import math
import random
import heapq, bisect
import sys
from collections import deque, defaultdict
from fractions import Fraction
import sys
import threading
from collections import defaultdict
mod = 10 ** 9 + 7
mod1 = 998244353
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192

class FastIO(IOBase):
	newlines = 0

	def __init__(self, file):
		self._fd = file.fileno()
		self.buffer = BytesIO()
		self.writable = 'x' in file.mode or 'r' not in file.mode
		self.write = self.buffer.write if self.writable else None

	def read(self):
		while True:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			if not b:
				break
			ptr = self.buffer.tell()
			(self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
		self.newlines = 0
		return self.buffer.read()

	def readline(self):
		while self.newlines == 0:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			self.newlines = b.count(b'\n') + (not b)
			ptr = self.buffer.tell()
			(self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
		self.newlines -= 1
		return self.buffer.readline()

	def flush(self):
		if self.writable:
			os.write(self._fd, self.buffer.getvalue())
			(self.buffer.truncate(0), self.buffer.seek(0))

class IOWrapper(IOBase):

	def __init__(self, file):
		self.buffer = FastIO(file)
		self.flush = self.buffer.flush
		self.writable = self.buffer.writable
		self.write = lambda s: self.buffer.write(s.encode('ascii'))
		self.read = lambda : self.buffer.read().decode('ascii')
		self.readline = lambda : self.buffer.readline().decode('ascii')
(sys.stdin, sys.stdout) = (IOWrapper(sys.stdin), IOWrapper(sys.stdout))
input = lambda : sys.stdin.readline().rstrip('\r\n')

class TreeNode:

	def __init__(self, k, v):
		self.key = k
		self.value = v
		self.left = None
		self.right = None
		self.parent = None
		self.height = 1
		self.num_left = 1
		self.num_total = 1

class AvlTree:

	def __init__(self):
		self._tree = None

	def add(self, k, v):
		if not self._tree:
			self._tree = TreeNode(k, v)
			return
		node = self._add(k, v)
		if node:
			self._rebalance(node)

	def _add(self, k, v):
		node = self._tree
		while node:
			if k < node.key:
				if node.left:
					node = node.left
				else:
					node.left = TreeNode(k, v)
					node.left.parent = node
					return node.left
			elif node.key < k:
				if node.right:
					node = node.right
				else:
					node.right = TreeNode(k, v)
					node.right.parent = node
					return node.right
			else:
				node.value = v
				return

	@staticmethod
	def get_height(x):
		return x.height if x else 0

	@staticmethod
	def get_num_total(x):
		return x.num_total if x else 0

	def _rebalance(self, node):
		n = node
		while n:
			lh = self.get_height(n.left)
			rh = self.get_height(n.right)
			n.height = max(lh, rh) + 1
			balance_factor = lh - rh
			n.num_total = 1 + self.get_num_total(n.left) + self.get_num_total(n.right)
			n.num_left = 1 + self.get_num_total(n.left)
			if balance_factor > 1:
				if self.get_height(n.left.left) < self.get_height(n.left.right):
					self._rotate_left(n.left)
				self._rotate_right(n)
			elif balance_factor < -1:
				if self.get_height(n.right.right) < self.get_height(n.right.left):
					self._rotate_right(n.right)
				self._rotate_left(n)
			else:
				n = n.parent

	def _remove_one(self, node):
		replacement = node.left or node.right
		if node.parent:
			if AvlTree._is_left(node):
				node.parent.left = replacement
			else:
				node.parent.right = replacement
			replacement.parent = node.parent
			node.parent = None
		else:
			self._tree = replacement
			replacement.parent = None
		node.left = None
		node.right = None
		node.parent = None
		self._rebalance(replacement)

	def _remove_leaf(self, node):
		if node.parent:
			if AvlTree._is_left(node):
				node.parent.left = None
			else:
				node.parent.right = None
			self._rebalance(node.parent)
		else:
			self._tree = None
		node.parent = None
		node.left = None
		node.right = None

	def remove(self, k):
		node = self._get_node(k)
		if not node:
			return
		if AvlTree._is_leaf(node):
			self._remove_leaf(node)
			return
		if node.left and node.right:
			nxt = AvlTree._get_next(node)
			node.key = nxt.key
			node.value = nxt.value
			if self._is_leaf(nxt):
				self._remove_leaf(nxt)
			else:
				self._remove_one(nxt)
			self._rebalance(node)
		else:
			self._remove_one(node)

	def get(self, k):
		node = self._get_node(k)
		return node.value if node else -1

	def _get_node(self, k):
		if not self._tree:
			return None
		node = self._tree
		while node:
			if k < node.key:
				node = node.left
			elif node.key < k:
				node = node.right
			else:
				return node
		return None

	def get_at(self, pos):
		x = pos + 1
		node = self._tree
		while node:
			if x < node.num_left:
				node = node.left
			elif node.num_left < x:
				x -= node.num_left
				node = node.right
			else:
				return (node.key, node.value)
		raise IndexError('Out of ranges')

	@staticmethod
	def _is_left(node):
		return node.parent.left and node.parent.left == node

	@staticmethod
	def _is_leaf(node):
		return node.left is None and node.right is None

	def _rotate_right(self, node):
		if not node.parent:
			self._tree = node.left
			node.left.parent = None
		elif AvlTree._is_left(node):
			node.parent.left = node.left
			node.left.parent = node.parent
		else:
			node.parent.right = node.left
			node.left.parent = node.parent
		bk = node.left.right
		node.left.right = node
		node.parent = node.left
		node.left = bk
		if bk:
			bk.parent = node
		node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1
		node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right)
		node.num_left = 1 + self.get_num_total(node.left)

	def _rotate_left(self, node):
		if not node.parent:
			self._tree = node.right
			node.right.parent = None
		elif AvlTree._is_left(node):
			node.parent.left = node.right
			node.right.parent = node.parent
		else:
			node.parent.right = node.right
			node.right.parent = node.parent
		bk = node.right.left
		node.right.left = node
		node.parent = node.right
		node.right = bk
		if bk:
			bk.parent = node
		node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1
		node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right)
		node.num_left = 1 + self.get_num_total(node.left)

	@staticmethod
	def _get_next(node):
		if not node.right:
			return node.parent
		n = node.right
		while n.left:
			n = n.left
		return n

class SegmentTree1:

	def __init__(self, data, default=300006, func=lambda a, b: min(a, b)):
		self._default = default
		self._func = func
		self._len = len(data)
		self._size = _size = 1 << (self._len - 1).bit_length()
		self.data = [default] * (2 * _size)
		self.data[_size:_size + self._len] = data
		for i in reversed(range(_size)):
			self.data[i] = func(self.data[i + i], self.data[i + i + 1])

	def __delitem__(self, idx):
		self[idx] = self._default

	def __getitem__(self, idx):
		return self.data[idx + self._size]

	def __setitem__(self, idx, value):
		idx += self._size
		self.data[idx] = value
		idx >>= 1
		while idx:
			self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
			idx >>= 1

	def __len__(self):
		return self._len

	def query(self, start, stop):
		if start == stop:
			return self.__getitem__(start)
		stop += 1
		start += self._size
		stop += self._size
		res = self._default
		while start < stop:
			if start & 1:
				res = self._func(res, self.data[start])
				start += 1
			if stop & 1:
				stop -= 1
				res = self._func(res, self.data[stop])
			start >>= 1
			stop >>= 1
		return res

	def __repr__(self):
		return 'SegmentTree({0})'.format(self.data)

class SegmentTree:

	def __init__(self, data, default=0, func=lambda a, b: a + b):
		self._default = default
		self._func = func
		self._len = len(data)
		self._size = _size = 1 << (self._len - 1).bit_length()
		self.data = [default] * (2 * _size)
		self.data[_size:_size + self._len] = data
		for i in reversed(range(_size)):
			self.data[i] = func(self.data[i + i], self.data[i + i + 1])

	def __delitem__(self, idx):
		self[idx] = self._default

	def __getitem__(self, idx):
		return self.data[idx + self._size]

	def __setitem__(self, idx, value):
		idx += self._size
		self.data[idx] = value
		idx >>= 1
		while idx:
			self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
			idx >>= 1

	def __len__(self):
		return self._len

	def query(self, start, stop):
		if start == stop:
			return self.__getitem__(start)
		stop += 1
		start += self._size
		stop += self._size
		res = self._default
		while start < stop:
			if start & 1:
				res = self._func(res, self.data[start])
				start += 1
			if stop & 1:
				stop -= 1
				res = self._func(res, self.data[stop])
			start >>= 1
			stop >>= 1
		return res

	def __repr__(self):
		return 'SegmentTree({0})'.format(self.data)

class Factorial:

	def __init__(self, MOD):
		self.MOD = MOD
		self.factorials = [1, 1]
		self.invModulos = [0, 1]
		self.invFactorial_ = [1, 1]

	def calc(self, n):
		if n <= -1:
			print('Invalid argument to calculate n!')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		if n < len(self.factorials):
			return self.factorials[n]
		nextArr = [0] * (n + 1 - len(self.factorials))
		initialI = len(self.factorials)
		prev = self.factorials[-1]
		m = self.MOD
		for i in range(initialI, n + 1):
			prev = nextArr[i - initialI] = prev * i % m
		self.factorials += nextArr
		return self.factorials[n]

	def inv(self, n):
		if n <= -1:
			print('Invalid argument to calculate n^(-1)')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		p = self.MOD
		pi = n % p
		if pi < len(self.invModulos):
			return self.invModulos[pi]
		nextArr = [0] * (n + 1 - len(self.invModulos))
		initialI = len(self.invModulos)
		for i in range(initialI, min(p, n + 1)):
			next = -self.invModulos[p % i] * (p // i) % p
			self.invModulos.append(next)
		return self.invModulos[pi]

	def invFactorial(self, n):
		if n <= -1:
			print('Invalid argument to calculate (n^(-1))!')
			print('n must be non-negative value. But the argument was ' + str(n))
			exit()
		if n < len(self.invFactorial_):
			return self.invFactorial_[n]
		self.inv(n)
		nextArr = [0] * (n + 1 - len(self.invFactorial_))
		initialI = len(self.invFactorial_)
		prev = self.invFactorial_[-1]
		p = self.MOD
		for i in range(initialI, n + 1):
			prev = nextArr[i - initialI] = prev * self.invModulos[i % p] % p
		self.invFactorial_ += nextArr
		return self.invFactorial_[n]

class Combination:

	def __init__(self, MOD):
		self.MOD = MOD
		self.factorial = Factorial(MOD)

	def ncr(self, n, k):
		if k < 0 or n < k:
			return 0
		k = min(k, n - k)
		f = self.factorial
		return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD

def powm(a, n, m):
	if a == 1 or n == 0:
		return 1
	if n % 2 == 0:
		s = powm(a, n // 2, m)
		return s * s % m
	else:
		return a * powm(a, n - 1, m) % m

def sort_list(list1, list2):
	zipped_pairs = zip(list2, list1)
	z = [x for (_, x) in sorted(zipped_pairs)]
	return z

def product(l):
	por = 1
	for i in range(len(l)):
		por *= l[i]
	return por

def binarySearchCount(arr, n, key):
	left = 0
	right = n - 1
	count = 0
	while left <= right:
		mid = int((right + left) / 2)
		if arr[mid] <= key:
			count = mid + 1
			left = mid + 1
		else:
			right = mid - 1
	return count

def countdig(n):
	c = 0
	while n > 0:
		n //= 10
		c += 1
	return c

def binary(x, length):
	y = bin(x)[2:]
	return y if len(y) >= length else '0' * (length - len(y)) + y

def countGreater(arr, n, k):
	l = 0
	r = n - 1
	leftGreater = n
	while l <= r:
		m = int(l + (r - l) / 2)
		if arr[m] >= k:
			leftGreater = m
			r = m - 1
		else:
			l = m + 1
	return n - leftGreater

class TrieNode:

	def __init__(self):
		self.children = [None] * 26
		self.isEndOfWord = False

class Trie:

	def __init__(self):
		self.root = self.getNode()

	def getNode(self):
		return TrieNode()

	def _charToIndex(self, ch):
		return ord(ch) - ord('a')

	def insert(self, key):
		pCrawl = self.root
		length = len(key)
		for level in range(length):
			index = self._charToIndex(key[level])
			if not pCrawl.children[index]:
				pCrawl.children[index] = self.getNode()
			pCrawl = pCrawl.children[index]
		pCrawl.isEndOfWord = True

	def search(self, key):
		pCrawl = self.root
		length = len(key)
		for level in range(length):
			index = self._charToIndex(key[level])
			if not pCrawl.children[index]:
				return False
			pCrawl = pCrawl.children[index]
		return pCrawl != None and pCrawl.isEndOfWord

class Node:

	def __init__(self, data):
		self.data = data
		self.count = 0
		self.left = None
		self.right = None

class BinaryTrie:

	def __init__(self):
		self.root = Node(0)

	def insert(self, pre_xor):
		self.temp = self.root
		for i in range(31, -1, -1):
			val = pre_xor & 1 << i
			if val:
				if not self.temp.right:
					self.temp.right = Node(0)
				self.temp = self.temp.right
				self.temp.count += 1
			if not val:
				if not self.temp.left:
					self.temp.left = Node(0)
				self.temp = self.temp.left
				self.temp.count += 1
		self.temp.data = pre_xor

	def query(self, xor):
		self.temp = self.root
		for i in range(31, -1, -1):
			val = xor & 1 << i
			if not val:
				if self.temp.left and self.temp.left.count > 0:
					self.temp = self.temp.left
				elif self.temp.right:
					self.temp = self.temp.right
			elif self.temp.right and self.temp.right.count > 0:
				self.temp = self.temp.right
			elif self.temp.left:
				self.temp = self.temp.left
			self.temp.count -= 1
		return xor ^ self.temp.data
(n, x, y) = map(int, input().split())
l = list(map(int, input().split()))
l = [(l[i], i + 1) for i in range(n)]
l.sort()
t = 1
f = -1
for i in range(n - 1, 0, -1):
	if l[i][0] * t >= x:
		f = i
		break
	t += 1
t = 1
f1 = -1
if f != -1:
	for i in range(f - 1, -1, -1):
		if l[i][0] * t >= y:
			f1 = i
			break
		t += 1
if f1 != -1:
	q = []
	q1 = []
	for i in range(f1, f):
		q.append(l[i][1])
	for i in range(f, n):
		q1.append(l[i][1])
	print('Yes')
	print(len(q1), len(q))
	print(*q1)
	print(*q)
	sys.exit(0)
t = 1
f = -1
for i in range(n - 1, 0, -1):
	if l[i][0] * t >= y:
		f = i
		break
	t += 1
t = 1
f1 = -1
if f != -1:
	for i in range(f - 1, -1, -1):
		if l[i][0] * t >= x:
			f1 = i
			break
		t += 1
if f1 != -1:
	q = []
	q1 = []
	for i in range(f1, f):
		q.append(l[i][1])
	for i in range(f, n):
		q1.append(l[i][1])
	print('Yes')
	print(len(q), len(q1))
	print(*q)
	print(*q1)
	sys.exit(0)
print('No')


def readline():
	return tuple(map(int, input().split()))

def ceil_div(num, den):
	return (num - 1) // den + 1

def main():
	(n, x1, x2) = readline()
	c = readline()
	xx = (x1, x2)
	servers = sorted(enumerate(c, start=1), key=lambda p: p[1])
	for (i, a) in enumerate(servers):
		for (j, x) in enumerate(xx):
			kj = ceil_div(x, a[1])
			if i + kj < n and (n - i - kj) * servers[i + kj][1] >= sum(xx) - x:
				print('Yes')
				l1 = servers[i:i + kj]
				l2 = servers[i + kj:]
				if j:
					(l1, l2) = (l2, l1)
				print(len(l1), len(l2))
				print(' '.join((str(d[0]) for d in l1)))
				print(' '.join((str(d[0]) for d in l2)))
				return
	print('No')
main()


(n, a, b) = [int(x) for x in input().split()]
hs = [int(x) for x in input().split()]
hs = sorted(enumerate(hs), key=lambda x: x[1])
for i in range(1, n + 1):
	if hs[-i][1] * i >= a:
		break
else:
	print('No')
	exit()
for j in range(i + 1, n + 1):
	if hs[-j][1] * (j - i) >= b:
		print('Yes')
		print(i, j - i)
		print(' '.join(map(str, [index + 1 for (index, _) in hs[-i:]])))
		print(' '.join(map(str, [index + 1 for (index, _) in hs[-j:-i]])))
		break
else:
	for i in range(1, n + 1):
		if hs[-i][1] * i >= b:
			break
	else:
		print('No')
		exit()
	for j in range(i + 1, n + 1):
		if hs[-j][1] * (j - i) >= a:
			print('Yes')
			print(j - i, i)
			print(' '.join(map(str, [index + 1 for (index, _) in hs[-j:-i]])))
			print(' '.join(map(str, [index + 1 for (index, _) in hs[-i:]])))
			break
	else:
		print('No')


(n, x1, x2) = map(int, input().split())
c = list(map(int, input().split()))
c = [(ci, i) for (i, ci) in enumerate(c)]
c.sort(reverse=True)

def check(x1, x2, reverse=False):
	sum1 = sum2 = 0
	i = i1 = i2 = 0
	while i < len(c):
		sum1 += c[i][0]
		i += 1
		if sum1 >= x1 and 1.0 * x1 / i <= c[i - 1][0]:
			break
	i1 = i
	if i1 == n:
		return False
	while i < len(c):
		sum2 += c[i][0]
		i += 1
		if sum2 >= x2 and 1.0 * x2 / (i - i1) <= c[i - 1][0]:
			print('Yes')
			if reverse:
				print(i - i1, i1)
				print(' '.join(map(str, [ci[1] + 1 for ci in c[i1:i]])))
				print(' '.join(map(str, [ci[1] + 1 for ci in c[:i1]])))
			else:
				print(i1, i - i1)
				print(' '.join(map(str, [ci[1] + 1 for ci in c[:i1]])))
				print(' '.join(map(str, [ci[1] + 1 for ci in c[i1:i]])))
			return True
	return False
if not (check(x1, x2) or check(x2, x1, reverse=True)):
	print('No')


def fin(c, x):
	return (x + c - 1) // c

def ck(x, b):
	r = (n, n)
	for i in range(b, n):
		r = min(r, (i + fin(c[i][0], x), i))
	return r

def sol(r, l):
	if r[0] <= n and l[0] <= n and (r[1] < n) and (l[1] < n):
		print('Yes')
		print(r[0] - r[1], l[0] - l[1])
		print(' '.join([str(x[1]) for x in c[r[1]:r[0]]]))
		print(' '.join([str(x[1]) for x in c[l[1]:l[0]]]))
		return True
	else:
		return False
(n, x1, x2) = [int(x) for x in input().split()]
c = sorted([(int(x), i + 1) for (i, x) in enumerate(input().split())])
r1 = ck(x1, 0)
l1 = ck(x2, r1[0])
r2 = ck(x2, 0)
l2 = ck(x1, r2[0])
if not sol(r1, l1) and (not sol(l2, r2)):
	print('No')


import collections
import time
import os
import sys
import bisect
import heapq
(n, x1, x2) = map(int, input().split())
C = [int(x) for x in input().split()]
C = [(v, i + 1) for (i, v) in enumerate(C)]
C.sort()

def check(x1, x2, rev):
	r = n
	(p1, p2) = ([], [])
	for i in range(n - 1, -1, -1):
		if C[i][0] * (n - i) >= x1:
			r = i
			p1 = [v[1] for v in C[i:]]
			break
	if p1:
		for i in range(r, -1, -1):
			if C[i][0] * (r - i) >= x2:
				p2 = [v[1] for v in C[i:r]]
				if rev:
					(p1, p2) = (p2, p1)
				print('Yes')
				print('{} {}'.format(len(p1), len(p2)))
				print(' '.join(map(str, p1)))
				print(' '.join(map(str, p2)))
				exit(0)
check(x1, x2, False)
check(x2, x1, True)
print('No')