import os
from collections import defaultdict

def countVerticalPaths(cost, edge_nodes, edge_from, edge_to, k):
# Write your code here

children = defaultdict(list)
for i in range(edge_nodes - 1):
u, v = edge_from[i] - 1, edge_to[i] - 1
children[u].append(v)
children[v].append(u)

prefixes = defaultdict(int)
prefixes[0] = 1
stack = [(0, 0, False)]
visited = [False] * edge_nodes
visited[0] = True
count = 0

while stack:
node, current_sum, is_backtrack = stack.pop()
if is_backtrack:
prefixes[(current_sum + cost[node]) % k] -= 1
continue

current_mod = (current_sum + cost[node]) % k
count += prefixes[current_mod]
prefixes[current_mod] += 1
stack.append((node, current_sum, True))

for child in children[node]:
if not visited[child]:
visited[child] = True
stack.append((child, current_mod, False))

return count


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def count_set_bits(number):
bit_mask = 1
set_bits_count = 0
for bit_position in range(32):
quotient = number // (bit_mask << (bit_position + 1))
remainder = number % (bit_mask << (bit_position + 1)) - (bit_mask << bit_position)
set_bits_count += quotient * (bit_mask << bit_position)
if remainder > 0:
set_bits_count += remainder
if (number >> bit_position) & 1:
set_bits_count += 1
return set_bits_count

def solve(target_count):
if target_count == 0:
return 1
low, high = 1, int(1e9) + 1
while low < high:
mid = (low + high) // 2
current_count = count_set_bits(mid)
if current_count >= target_count + 1:
high = mid
else:
low = mid + 1
return low

def get_value_at_indices(queries):
results = []
for query in queries:
result = solve(query)
results.append(result)
return results

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