Harryxun/testdata huggingface dataset:
Buggy python submission (verdict: Time Limit Exceeded):
def main():
	n = int(input())
	r = [0]*5
	r[0] = int(input())
	r[1] = int(input())
	r[2] = int(input())
	r[3] = int(input())
	r[4] = int(input())
	dp = [n, 0, 0, 0, 0, 0]
	time = 0
	while True:
		time += 1
		for i in range(5, 0, -1):
			if dp[i-1] != 0:
				move = min(r[i-1], dp[i-1])
				dp[i] += move
				dp[i-1] -= move
		if dp[5] == n:
			break
	print(time)

if __name__ == '__main__':
    main()

Fixed submission:
def main():
	n = int(input())
	r = [0]*5
	r[0] = int(input())
	r[1] = int(input())
	r[2] = int(input())
	r[3] = int(input())
	r[4] = int(input())
	total = 4
	min_r = min(r)
	div = n // min_r
	mod = n % min_r
	total += div
	if mod != 0:
		total += 1

	print(total)

if __name__ == '__main__':
    main()
Buggy python submission (verdict: Time Limit Exceeded):
def main():
	x, y, z, k = map(int, input().split())
	a = list(map(int, input().split()))
	b = list(map(int, input().split()))
	c = list(map(int, input().split()))
	d = [0]*x*y
	for i in range(x):
		for j in range(y):
			d[i*y+j] = a[i]+b[j]
	d.sort(reverse=True)
	c.sort(reverse=True)

	c_len = min(k, z)
	d_len = min(k, x*y)
	e = [0]*d_len*c_len
	for i in range(d_len):
		for j in range(c_len):
			e[i*c_len+j] = d[i] + c[j]
	e.sort(reverse=True)
	for i in range(k):
		print(e[i])


if __name__ == '__main__':
    main()

Fixed submission:
def main():
	x, y, z, k = map(int, input().split())
	a = list(map(int, input().split()))
	b = list(map(int, input().split()))
	c = list(map(int, input().split()))
	d = [0]*x*y
	for i in range(x):
		for j in range(y):
			d[i*y+j] = a[i]+b[j]
	d.sort(reverse=True)
	c.sort(reverse=True)

	c_len = min(k, z)
	d_len = min(k, x*y)
	e = [0]*d_len*c_len
	for i in range(d_len):
		for j in range(c_len):
			e[i*c_len+j] = d[i] + c[j]
	e.sort(reverse=True)
	for i in range(k):
		print(e[i])


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
import sys
def main():
	sys.setrecursionlimit(10**9)
	x, y, z, k = map(int, input().split())
	a = list(map(int, input().split()))
	b = list(map(int, input().split()))
	c = list(map(int, input().split()))
	d = [0]*x*y*z
	for i in range(x):
		for j in range(y):
			for l in range(z):
				d[i*y*z+j*z+l] = a[i]+b[j]+c[l]
	d.sort(reverse=True)
	for i in range(k):
		print(d[i])


if __name__ == '__main__':
    main()

Fixed submission:
def main():
	x, y, z, k = map(int, input().split())
	a = list(map(int, input().split()))
	b = list(map(int, input().split()))
	c = list(map(int, input().split()))
	d = [0]*x*y
	for i in range(x):
		for j in range(y):
			d[i*y+j] = a[i]+b[j]
	d.sort(reverse=True)
	c.sort(reverse=True)

	c_len = min(k, z)
	d_len = min(k, x*y)
	e = [0]*d_len*c_len
	for i in range(d_len):
		for j in range(c_len):
			e[i*c_len+j] = d[i] + c[j]
	e.sort(reverse=True)
	for i in range(k):
		print(e[i])


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
import heapq

def main():
	x, y, z, k = map(int, input().split())
	a = list(map(int, input().split()))
	b = list(map(int, input().split()))
	c = list(map(int, input().split()))
	d = [0]*x*y*z
	for i in range(x):
		for j in range(y):
			for l in range(z):
				d[i*y*z+j*z+l] = a[i]+b[j]+c[l]
	d.sort(reverse=True)
	for i in range(k):
		print(d[i])


if __name__ == '__main__':
    main()

Fixed submission:
def main():
	x, y, z, k = map(int, input().split())
	a = list(map(int, input().split()))
	b = list(map(int, input().split()))
	c = list(map(int, input().split()))
	d = [0]*x*y
	for i in range(x):
		for j in range(y):
			d[i*y+j] = a[i]+b[j]
	d.sort(reverse=True)
	c.sort(reverse=True)

	c_len = min(k, z)
	d_len = min(k, x*y)
	e = [0]*d_len*c_len
	for i in range(d_len):
		for j in range(c_len):
			e[i*c_len+j] = d[i] + c[j]
	e.sort(reverse=True)
	for i in range(k):
		print(e[i])


if __name__ == '__main__':
    main()
Buggy python submission (verdict: Runtime Error):
def main():
	n, q = map(int, input().split())
	s = input()
	acs = [0]*(n+1)
	for i in range(1, n+1):
		if s[i-1] == "A" and s[i] == "C":
			acs[i] = acs[i-1] + 1
		else:
			acs[i] = acs[i-1]
	results = [0]*q
	for i in range(q):
		l, r = map(int, input().split())
		if l == r:
			continue

		results[i] = acs[r] - acs[l]
		if s[r-1] == "A":
			results[i] -= 1
		if s[l-1] == "A" and s[l] == "C":
			results[i] += 1
	for result in results:
		print(result)

if __name__ == '__main__':
    main()

Fixed submission:
def main():
	n, q = map(int, input().split())
	s = input()
	acs = [0]*(n)
	for i in range(1, n):
		if s[i-1] == "A" and s[i] == "C":
			acs[i] = acs[i-1] + 1
		else:
			acs[i] = acs[i-1]
	results = [0]*q
	for i in range(q):
		l, r = map(int, input().split())
		if l == r:
			continue
		results[i] = acs[r-1] - acs[l-1]
	for result in results:
		print(result)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
def main():
	n, q = map(int, input().split())
	s = input()
	acs = [0]*(n+1)
	for i in range(1, n+1):
		if s[i-1] == "A" and s[i] == "C":
			acs[i] = acs[i-1] + 1
		else:
			acs[i] = acs[i-1]
	results = [0]*q
	for i in range(q):
		l, r = map(int, input().split())
		results[i] = acs[r] - acs[l]
		if s[r-1] == "A" and l != r:
			results[i] -= 1
		if s[l-1] == "A" and l != r:
			results[i] += 1
	for result in results:
		print(result)

if __name__ == '__main__':
    main()

Fixed submission:
def main():
	n, q = map(int, input().split())
	s = input()
	acs = [0]*(n)
	for i in range(1, n):
		if s[i-1] == "A" and s[i] == "C":
			acs[i] = acs[i-1] + 1
		else:
			acs[i] = acs[i-1]
	results = [0]*q
	for i in range(q):
		l, r = map(int, input().split())
		if l == r:
			continue
		results[i] = acs[r-1] - acs[l-1]
	for result in results:
		print(result)

if __name__ == '__main__':
    main()
Buggy python submission (verdict: Time Limit Exceeded):
import collections
def main():
	n, m = map(int, input().split())
	bridge = [[0, 0]]*m
	for i in range(m):
		bridge[i] = list(map(int, input().split()))
	inconveniences = [0]*(m+1)
	inconveniences[m] = (n*(n-1))//2
	islands = collections.defaultdict(list)
	stack = []
	for i in range(m-1, -1, -1):
		if inconveniences[i+1] == 0:
			break

		does_route_exist = False
		for island in islands[bridge[i][0]]:
			if island == bridge[i][1]:
				does_route_exist = True
				break

		if does_route_exist:
			inconvenience[i] = inconveniences[i+1]
			continue

		islands[bridge[i][0]].append(bridge[i][1])
		islands[bridge[i][1]].append(bridge[i][0])
		stack.append(bridge[i][0])

		is_visited = [False]*(n+1)
		total = 0
		for s in stack:
			is_visited[s] = True
			island_pair = 0
			queue = collections.deque([s])
			while queue:
				for island in islands[queue.popleft()]:
					if is_visited[island]:
						continue
					queue.append(island)
					is_visited[island] = True
					island_pair += 1

			total += (island_pair*(island_pair+1))//2

		inconveniences[i] = inconveniences[m] - total

	for i in range(1, m+1):
		print(inconveniences[i])

if __name__ == '__main__':
    main()

Fixed submission:
def main():
	n, m = map(int, input().split())
	bridge = [[0, 0]]*m
	for i in range(m):
		bridge[i] = list(map(int, input().split()))
	inconveniences = [0]*(m+1)
	inconveniences[m] = (n*(n-1))//2
	union_find = [[i, 0, 1] for i in range(n+1)]

	for i in range(m-1, -1, -1):
		if inconveniences[i+1] == 0:
			break
		if same(union_find, bridge[i][0], bridge[i][1]):
			inconveniences[i] = inconveniences[i+1]
			continue
		rx = root(union_find, bridge[i][0])
		ry = root(union_find, bridge[i][1])
		inconveniences[i] = inconveniences[i+1] - union_find[rx][2]*union_find[ry][2]
		unite(union_find, bridge[i][0], bridge[i][1])

	for i in range(1, m+1):
		print(inconveniences[i])

def root(union_find, val:int) -> int:
	if union_find[val][0] == val:
		return val
	return root(union_find, union_find[val][0])

def same(union_find, x:int, y:int) -> bool:
	rx = root(union_find, x)
	ry = root(union_find, y)
	return rx == ry

def unite(union_find, x:int, y:int):
	rx = root(union_find, x)
	ry = root(union_find, y)
	if rx == ry:
		return
	if union_find[rx][1] < union_find[ry][1]:
		union_find[rx][0] = ry
		union_find[ry][2] += union_find[rx][2]
	else:
		union_find[ry][0] = rx
		union_find[rx][2] += union_find[ry][2]
		if union_find[rx][1] == union_find[ry][1]:
			union_find[rx][1] += 1

if __name__ == '__main__':
    main()
Buggy python submission (verdict: Runtime Error):
def main():
	a,b = map(int, input().split())
	if (b %= a) == 0:
		print(a+b)
	else:
		print(b-a)

if __name__ == '__main__':
	main()

Fixed submission:
def main():
	a,b = map(int, input().split())
	if (b % a) == 0:
		print(a+b)
	else:
		print(b-a)

if __name__ == '__main__':
	main()

Buggy python submission (verdict: Runtime Error):
def main():
	s = input().strip()
	a = s[0]
	b = s[1]
	if (b/a)*a == b:
		print(a+b)
	else:
		print(b-a)

if __name__ == '__main__':
	main()

Fixed submission:
def main():
	a,b = map(int, input().split())
	if (b % a) == 0:
		print(a+b)
	else:
		print(b-a)

if __name__ == '__main__':
	main()
Buggy python submission (verdict: Runtime Error):
def main():
	n = int(input())
	xi, yi, hi = [0]*n, [0]*n, [0]*n
	stack = []
	result = []
	for i in range(n):
		xi[i], yi[i], hi[i] = map(int, input().split())
		if hi[i] > 0:
			stack = [xi[i], yi[i], hi[i]]
	for i in range(101):
		for j in range(101):
			guess = stack[2] + abs(stack[0]-i) + abs(stack[1]-j)
			is_result = True
			for k in range(n):
				result = guess - abs(xi[k]-i) - abs(yi[k]-j)
				result = max(result, 0)
				if hi[k] != result:
					is_result = False
					break
			if is_result:
				print(str(i)+" "+str(j)+" "+str(v))
				return


if __name__ == '__main__':
    main()

Fixed submission:
def main():
	n = int(input())
	xi, yi, hi = [0]*n, [0]*n, [0]*n
	stack = []
	result = []
	for i in range(n):
		xi[i], yi[i], hi[i] = map(int, input().split())
		if hi[i] > 0:
			stack = [xi[i], yi[i], hi[i]]
	for i in range(101):
		for j in range(101):
			guess = stack[2] + abs(stack[0]-i) + abs(stack[1]-j)
			is_result = True
			for k in range(n):
				result = guess - abs(xi[k]-i) - abs(yi[k]-j)
				result = max(result, 0)
				if hi[k] != result:
					is_result = False
					break
			if is_result:
				print(str(i)+" "+str(j)+" "+str(guess))
				return


if __name__ == '__main__':
    main()
Buggy python submission (verdict: Time Limit Exceeded):
def main():
	N, M, Q = map(int, input().split())
	LR = [[0 for _ in range(N+1)] for _ in range(N+1)]
	ans = [0]*Q
	for _ in range(M):
		l, r = map(int, input().split())
		LR[l][r] += 1
	for i in range(Q):
		p, q = map(int, input().split())
		for a in range(p, q+1):
			for b in range(a, q+1):
				ans[i] += LR[a][b]
	for a in ans:
		print(a)


if __name__ == '__main__':
    main()

Fixed submission:
def main():
	N, M, Q = map(int, input().split())
	LR = [[0 for _ in range(N+1)] for _ in range(N+1)]
	ans = [0]*Q
	for _ in range(M):
		l, r = map(int, input().split())
		LR[l][r] += 1
	for i in range(1, N+1):
		for j in range(1, N+1):
			LR[i][j] += LR[i][j-1]
	for i in range(1, N+1):
		for j in range(1, N+1):
			LR[i][j] += LR[i-1][j]

	for i in range(Q):
		p, q = map(int, input().split())
		ans[i] = LR[q][q] + LR[p-1][p-1] - LR[p-1][q] - LR[q][p-1]
	for a in ans:
		print(a)


if __name__ == '__main__':
    main()
Buggy python submission (verdict: Runtime Error):
def main():
	N, M = map(int, input().split())
	A = list(map(int, input().split()))
	sums = [0]*(N+1)
	ans = 0
	mod = [0]*M
	mod[0] = 1
	for i in range(1, N+1):
		sums[i] = (sums[i-1] + A[i-1]) % M
		ans += mod[sums[i]]
		mod[sums[i]] += 1

	print(ans)

if __name__ == '__main__':
    main()

Fixed submission:
from collections import defaultdict
def main():
	N, M = map(int, input().split())
	A = list(map(int, input().split()))
	sums = [0]*(N+1)
	ans = 0
	mod = defaultdict(int)
	mod[0] = 1
	for i in range(1, N+1):
		sums[i] = (sums[i-1] + A[i-1]) % M
		ans += mod[sums[i]]
		mod[sums[i]] += 1

	print(ans)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
def main():
	N, M = map(int, input().split())
	A = list(map(int, input().split()))
	sums = [0]*(N+1)
	for i in range(N+1):
		sums[i] = sums[i-1] + A[i-1]

	ans = 0
	for i in range(N+1):
		for j in range(i+1, N+1):
			if (sums[j] - sums[i]) % M == 0:
				ans += 1
	print(ans)

if __name__ == '__main__':
    main()

Fixed submission:
from collections import defaultdict
def main():
	N, M = map(int, input().split())
	A = list(map(int, input().split()))
	sums = [0]*(N+1)
	ans = 0
	mod = defaultdict(int)
	mod[0] = 1
	for i in range(1, N+1):
		sums[i] = (sums[i-1] + A[i-1]) % M
		ans += mod[sums[i]]
		mod[sums[i]] += 1

	print(ans)

if __name__ == '__main__':
    main()
Buggy python submission (verdict: Runtime Error):
def main():
	N = int(input())
	A = list(map(int, input().split()))
	for i in range(N):
		A[i] -= i+1
	A.sort()

	mid1 = A[N//2]
	mid2 = A[N//2 + 1]
	ans1 = 0
	ans2 = 0
	for i in range(N):
		ans1 += abs(A[i] - mid1)
		ans2 += abs(A[i] - mid2)

	print(min(ans1, ans2))


if __name__ == '__main__':
    main()

Fixed submission:
def main():
	N = int(input())
	A = list(map(int, input().split()))
	for i in range(N):
		A[i] -= i+1
	A.sort()


	mid1 = A[N//2]
	mid2 = A[N//2]
	if N >= 2:
		mid2 = A[N//2 + 1]

	ans1 = 0
	ans2 = 0
	for i in range(N):
		ans1 += abs(A[i] - mid1)
		ans2 += abs(A[i] - mid2)

	print(min(ans1, ans2))


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
def main():
	N = int(input())
	A = list(map(int, input().split()))
	ans = 0
	max_val = 0
	for i in range(N):
		ans += abs(A[i]-(i+1))
		max_val = max(max_val, abs(A[i]-(i+1)))

	for j in range(-max_val, max_val+1):
		this_ans = 0
		for i in range(N):
			this_ans += abs(A[i]-(i+j+1))
		ans = min(ans, this_ans)
	print(ans)


if __name__ == '__main__':
    main()

Fixed submission:
def main():
	N = int(input())
	A = list(map(int, input().split()))
	for i in range(N):
		A[i] -= i+1
	A.sort()


	mid1 = A[N//2]
	mid2 = A[N//2]
	if N >= 2:
		mid2 = A[N//2 + 1]

	ans1 = 0
	ans2 = 0
	for i in range(N):
		ans1 += abs(A[i] - mid1)
		ans2 += abs(A[i] - mid2)

	print(min(ans1, ans2))


if __name__ == '__main__':
    main()
Buggy python submission (verdict: Runtime Error):
def main():
	D, N = map(int, input().split())
	if N == 100:
		N += 1
	print(N * (100**D)

if __name__ == '__main__':
	main()

Fixed submission:
def main():
	D, N = map(int, input().split())
	if N == 100:
		N += 1
	print(N * (100**D))

if __name__ == '__main__':
	main()
Buggy python submission (verdict: Time Limit Exceeded):
def main():
	S = input()
	K = int(input())
	sub = set()
	for i in range(len(S)):
		for j in range(i+1, len(S)+1):
			sub.add(S[i:j])
	sub_list = list(sub)
	sub_list.sort()
	ans = sub_list[K-1]
	print(ans)

if __name__ == '__main__':
    main()

Fixed submission:
from collections import defaultdict
def main():
	S = input()
	K = int(input())
	sub = defaultdict(set)
	for i in range(len(S)):
		sub[S[i]].add(S[i:len(S)+1])

	alphabet = [chr(ord('a') + i) for i in range(26)]
	ans = set()
	for c in alphabet:
		if c in sub:
			this_list = list(sub[c])
			this_list.sort()
			for e in this_list:
				for i in range(1, len(e)+1):
					ans.add(e[:i])
					if len(ans) == K:
						print(e[:i])
						return


if __name__ == '__main__':
    main()
Buggy python submission (verdict: Time Limit Exceeded):
def main():
	N = int(input())
	A = list(map(int,input().split()))
	B = list(map(int,input().split()))
	ans = 0
	p = 1
	for k in range(29):
		a_m = sorted([i & (2*p-1) for i in A], reverse=True)
		b_m = sorted([i & (2*p-1) for i in B])
		s = 0
		l1 = 0
		r1 = 0
		l2 = 0
		r2 = 0
		for a in a_m:
			while l1 < N and a + b_m[l1] < p:
				l1 += 1
			while r1 < N and a + b_m[r1] < 2*p:
				r1 += 1
			while l2 < N and a + b_m[l2] < 3*p:
				l2 += 1
			while r2 < N and a + b_m[r2] < 4*p:
				r2 += 1
			s += r2 - l2 + r1 - l1
		if s&1 == 1:
			ans += p
		p *= 2

	print(ans)


if __name__ == '__main__':
    main()

Fixed submission:
def main():
	N = int(input())
	A = list(map(int,input().split()))
	B = list(map(int,input().split()))
	ans = 0
	p = 1
	for k in range(29):
		a_m = sorted([i & (2*p-1) for i in A], reverse=True)
		b_m = sorted([i & (2*p-1) for i in B])
		s = 0
		l1 = 0
		r1 = 0
		l2 = 0
		r2 = 0
		for a in a_m:
			while l1 < N and a + b_m[l1] < p:
				l1 += 1
			while r1 < N and a + b_m[r1] < 2*p:
				r1 += 1
			while l2 < N and a + b_m[l2] < 3*p:
				l2 += 1
			while r2 < N and a + b_m[r2] < 4*p:
				r2 += 1
			s += r2 - l2 + r1 - l1
		if s&1 == 1:
			ans += p
		p *= 2

	print(ans)


if __name__ == '__main__':
    main()
Buggy python submission (verdict: Runtime Error):
def main():
	H, W = map(int,input().split())
	pos = [""]*H
	for i in range(H):
		pos[i] = input()
	x = min(W, H)
	can_clear = True
	for dist in range(H+W-1):
		impossible_range = True
		for i in range(H):
			if i > dist:
				break
			if dist-i > W:
				continue
			if pos[i][dist-i] == ".":
				impossible_range = False
				break
		if impossible_range:
			can_clear = False
			break
	if not can_clear:
		print(-1)
		return

	offset = [[-1, 0], [1, 0], [0, -1], [0, 1]]
	def bfs(s, h, w):
		queue = [[0, 0, 0]]
		is_visited = [[False for _ in range(w)] for _ in range(h)]
		is_visited[0][0] = True
		while queue:
			cur = queue.pop(0)
			for o in offset:
				y, x = cur[0]+o[0], cur[1]+o[1]
				if x < 0 or x >= w or y < 0 or y >= h:
					continue
				if x == w-1 and y == h-1:
					return cur[2]+1
				if is_visited[y][x]:
					continue
				if s[y][x] == ".":
					queue.append([y, x, cur[2]+1])
					is_visited[y][x] = True
		return -1

	white_num = 0
	for i in range(H):
		for j in range(W):
			if pos[i][j] == ".":
				white_num += 1
	print(white_num-bfs(pos, H, W)-1)

if __name__ == '__main__':
    main()

Fixed submission:
def main():
	H, W = map(int,input().split())
	pos = [""]*H
	for i in range(H):
		pos[i] = input()

	offset = [[-1, 0], [1, 0], [0, -1], [0, 1]]
	def bfs(s, h, w):
		queue = [[0, 0, 0]]
		is_visited = [[False for _ in range(w)] for _ in range(h)]
		is_visited[0][0] = True
		while queue:
			cur = queue.pop(0)
			for o in offset:
				y, x = cur[0]+o[0], cur[1]+o[1]
				if x < 0 or x >= w or y < 0 or y >= h:
					continue
				if x == w-1 and y == h-1:
					return cur[2]+1
				if is_visited[y][x]:
					continue
				if s[y][x] == ".":
					queue.append([y, x, cur[2]+1])
					is_visited[y][x] = True
		return -1

	white_num = 0
	for i in range(H):
		for j in range(W):
			if pos[i][j] == ".":
				white_num += 1
	route = bfs(pos, H, W)
	if route == -1:
		print(-1)
	else:
		print(white_num-route-1)

if __name__ == '__main__':
    main()
Buggy python submission (verdict: Time Limit Exceeded):
def main():
	N, M = map(int,input().split())
	INF = 10**9+7
	if M == 0:
		print("Yes")
		return
	x = [[INF for _ in range(N)] for _ in range(N)]
	for i in range(M):
		l, r, d = map(int, input().split())
		l, r = l-1, r-1
		x[l][r] = d
		x[r][l] = -d
	ans_exist = True
	for k in range(N):
		for i in range(N):
			for j in range(N):
				if x[i][j] == INF:
					continue
				x[i][j] = min(x[i][j], x[i][k]+x[k][j])

	for i in range(N):
		for j in range(N):
			if x[i][j] == x[j][i] and x[i][j] == INF:
				continue
			if x[i][j] != -x[j][i]:
				ans_exist = False
				break
	if ans_exist:
		print("Yes")
	else:
		print("No")


if __name__ == '__main__':
    main()

Fixed submission:
def main():
	N, M = map(int,input().split())
	if M == 0:
		print("Yes")
		return
	x = [[] for _ in range(N)]
	ans = [0 for _ in range(N)]
	for i in range(M):
		l, r, d = map(int, input().split())
		l, r = l-1, r-1
		x[l].append([r, d])
		x[r].append([l, -d])

	visited = [False for _ in range(N)]

	def dfs(i):
		vs = [i]
		while vs:
			v = vs.pop()
			for nex in x[v]:
				if not visited[nex[0]]:
					visited[nex[0]] = True
					ans[nex[0]] = ans[v]+nex[1]
					vs.append(nex[0])
				else:
					if ans[nex[0]] != ans[v]+nex[1]:
						return False
		return True

	ans_exist = True
	for i in range(N):
		if not visited[i]:
			visited[i] = True
			ans_exist = dfs(i)
		if not ans_exist:
			break

	if ans_exist:
		print("Yes")
	else:
		print("No")


if __name__ == '__main__':
    main()
Buggy python submission (verdict: Runtime Error):
def main():
	N, K = map(int,input().split())
	points = [0]*N
	max_x, max_y, min_x, min_y = -10**9, -10**9, 10**9, 10**9
	for i in range(N):
		points[i] = list(map(int, input().split()))
		max_x = max(max_x, points[i][0])
		min_x = min(min_x, points[i][0])
		max_y = max(max_y, points[i][1])
		min_y = min(min_y, points[i][1])

	points.sort(key=lambda x:x[0])
	ans = (max_x-min_x)*(max_y-min_y)
	for lr in range(1, N-K+1):
		for l in range(lr):
			this_points = list(points[l:N-lr+l])
			w = this_points[-1][0]-this_points[0][0]
			if w <= 0:
				continue
			this_points.sort(key=lambda x:x[1])
			for t in range(N-K-lr+1):
				h = this_points[t+N-K-lr-1][1] - this_points[t][1]
				if h <= 0:
					continue
				ans = min(ans, w*h)
	print(ans)


if __name__ == '__main__':
    main()

Fixed submission:
def main():
	N, K = map(int,input().split())
	points = [0]*N
	max_x, max_y, min_x, min_y = -10**9, -10**9, 10**9, 10**9
	for i in range(N):
		points[i] = list(map(int, input().split()))
		max_x = max(max_x, points[i][0])
		min_x = min(min_x, points[i][0])
		max_y = max(max_y, points[i][1])
		min_y = min(min_y, points[i][1])

	points.sort(key=lambda x:x[0])
	ans = (max_x-min_x)*(max_y-min_y)
	for r in range(K, N+1):
		for l in range(N-r+1):
			w = points[r+l-1][0] - points[l][0]
			this_points = sorted(list(points[l:l+r]), key=lambda x:x[1])
			for b in range(r-K+1):
				h = this_points[b+K-1][1] - this_points[b][1]
				ans = min(ans, w*h)
	print(ans)


if __name__ == '__main__':
    main()
Buggy python submission (verdict: Time Limit Exceeded):
def main():
	X = int(input())
	cur = 0
	p = 0
	for _ in range(X):
		if cur == p:
			cur += 1
			p = 1
		else:
			p += 1
	print(cur)


if __name__ == '__main__':
    main()

Fixed submission:
def main():
	X = int(input())
	i = 1
	while (i*(i+1))//2 < X:
		i += 1
	print(i)


if __name__ == '__main__':
    main()
Buggy python submission (verdict: Runtime Error):
def main():
	N, K = map(int,input().split())
	A = list(map(int,input().split()))
	A.sort()
	l, r = 0, N-1
	while l < r:
		m = (l+r)>>1
		p = True
		if m == 0 and solve(N, K, A[1:], A[0]):
			l = m+1
			continue
		if solve(N, K, A[:m]+A[m+1:], A[m]):
			l = m+1
		else:
			r = m
	if l == N-1 and solve(N, K, A[:N-1], A[N-1]):
		l = N
	print(l)


def solve(n, k, a, ai):
	dp = [[False for _ in range(k+1)] for _ in range(n)]
	dp[0][0] = True
	if a[0] > k:
		dp[0][k] = True
	else:
		dp[0][a[0]] = True
	for i in range(1, n-1):
		for j in range(k-1):
			if not dp[i-1][j]:
				continue
			dp[i][j] = True
			if j + a[i] > k:
				dp[i][k] = True
			else:
				dp[i][j+a[i]] = True
	return not any(map(lambda j: dp[n-2][j], range(k-ai, k)))


if __name__ == '__main__':
    main()

Fixed submission:
def main():
	N, K = map(int,input().split())
	A = list(map(int,input().split()))
	A.sort(reverse=True)
	no_need = 0
	sub = 0
	for ai in A:
		if sub+ai < K:
			sub += ai
			no_need += 1
		else:
			no_need = 0

	print(no_need)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
def main():
	N, K = map(int,input().split())
	A = list(map(int,input().split()))
	A.sort()
	l, r = 0, N-1
	while l < r:
		m = (l+r)>>1
		p = True
		if solve(N, K, A[:m]+A[m+1:], A[m]):
			l = m+1
		else:
			r = m
	if l == N-1 and solve(N, K, A[:N-1], A[N-1]):
		l = N
	print(l)


def solve(n, k, a, ai):
	dp = [[False for _ in range(k+1)] for _ in range(n)]
	dp[0][0] = True
	if a[0] > k:
		dp[0][k] = True
	else:
		dp[0][a[0]] = True
	for i in range(1, n-1):
		for j in range(k-1):
			if not dp[i-1][j]:
				continue
			dp[i][j] = True
			if j + a[i] > k:
				dp[i][k] = True
			else:
				dp[i][j+a[i]] = True
	return not any(map(lambda j: dp[n-2][j], range(k-ai, k)))


if __name__ == '__main__':
    main()

Fixed submission:
def main():
	N, K = map(int,input().split())
	A = list(map(int,input().split()))
	A.sort(reverse=True)
	no_need = 0
	sub = 0
	for ai in A:
		if sub+ai < K:
			sub += ai
			no_need += 1
		else:
			no_need = 0

	print(no_need)


if __name__ == '__main__':
    main()