Social Infrastructure Information Systems Division  Hitachi Programming Contest 2020 - Manga Market

There are N stores called Store 1, Store 2, \cdots, Store N. Takahashi, who is at his house at time 0, is planning to visit some of these stores.

It takes Takahashi one unit of time to travel from his house to one of the stores, or between any two stores.

If Takahashi reaches Store i at time t, he can do shopping there after standing in a queue for a_i \times t + b_i units of time. (We assume that it takes no time other than waiting.)

All the stores close at time T + 0.5. If Takahashi is standing in a queue for some store then, he cannot do shopping there.

Takahashi does not do shopping more than once in the same store.

Find the maximum number of times he can do shopping before time T + 0.5.

Constraints

* All values in input are integers.
* 1 \leq N \leq 2 \times 10^5
* 0 \leq a_i \leq 10^9
* 0 \leq b_i \leq 10^9
* 0 \leq T \leq 10^9

Input

Input is given from Standard Input in the following format:


N T
a_1 b_1
a_2 b_2
\vdots
a_N b_N


Output

Print the answer.

Examples

Input

3 7
2 0
3 2
0 3


Output

2


Input

1 3
0 3


Output

0


Input

5 21600
2 14
3 22
1 3
1 10
1 9


Output

5


Input

7 57
0 25
3 10
2 4
5 15
3 22
2 14
1 15


Output

3

Difficulty: UNKNOWN_DIFFICULTY

Starter code:

Solutions:
import sys
readline = sys.stdin.buffer.readline
INF = 10 ** 18 + 3
(N, T) = map(int, readline().split())
AB = [tuple(map(int, readline().split())) for _ in range(N)]
ABzero = [b for (a, b) in AB if a == 0]
ABnonzero = [(a, b) for (a, b) in AB if a]
ABnonzero.sort(key=lambda x: (x[1] + 1) / x[0])
dp = [0]
for (a, b) in ABnonzero:
	dp2 = dp + [INF]
	for j in range(1, len(dp2)):
		dp2[j] = min(dp2[j], (dp[j - 1] + 1) * (a + 1) + b)
	dp = [d for d in dp2 if d <= T]
ABzero.sort()
dpzero = [0] + [b + 1 for b in ABzero]
for i in range(1, len(dpzero)):
	dpzero[i] += dpzero[i - 1]
DP = [INF] * (N + 1)
for i in range(len(dp)):
	for j in range(len(dpzero)):
		DP[i + j] = min(DP[i + j], dp[i] + dpzero[j])
DP = [d for d in DP if d <= T]
print(max(0, len(DP) - 1))


(N, T) = map(int, input().split())
kab = []
azero = []
for i in range(N):
	(a, b) = map(int, input().split())
	if a == 0:
		azero.append(b)
	else:
		k = a / (1 + b)
		kab.append([-1 * k, a, b])
nt = 0
kab.sort()
dp = [float('inf')] * 29
dp[0] = 0
for (k, a, b) in kab:
	for i in range(27, -1, -1):
		dp[i + 1] = min(dp[i + 1], 1 + dp[i] + a * (1 + dp[i]) + b)
azero.sort()
dsum = [0]
for i in azero:
	dsum.append(dsum[-1] + 1 + i)
ans = 0
import bisect
for i in range(29):
	if dp[i] > T:
		break
	else:
		ans = max(i + bisect.bisect_right(dsum, T - dp[i]) - 1, ans)
print(ans)


import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
from functools import cmp_to_key
import itertools
(N, T) = map(int, readline().split())
m = map(int, read().split())
AB0 = []
AB1 = []
for (a, b) in zip(m, m):
	if a == 0:
		AB0.append(b)
	else:
		AB1.append((a, b))

def sort_func(ab0, ab1):
	(a0, b0) = ab0
	(a1, b1) = ab1
	return a1 * (1 + b0) - a0 * (1 + b1)
AB0.sort()
AB1.sort(key=lambda x: x[0] / (x[1] + 1), reverse=True)
(AB0, AB1)

def compute_0():
	INF = T + 1
	dp = [INF] * 40
	dp[0] = 0
	for (a, b) in AB1:
		for n in range(39, -1, -1):
			if dp[n] > T:
				continue
			x = (dp[n] + 1) * (a + 1) + b
			if x < dp[n + 1]:
				dp[n + 1] = x
	return dp

def compute_1():
	return [0] + list(itertools.accumulate((x + 1 for x in AB0)))
dp0 = compute_0()
dp1 = compute_1()
R = len(dp1) - 1
answer = 0
for (i, x) in enumerate(dp0):
	if x > T:
		break
	while x + dp1[R] > T:
		R -= 1
	value = i + R
	if answer < value:
		answer = value
print(answer)


(n, t) = map(int, input().split())
ab = [list(map(int, input().split())) for i in range(n)]
ab0 = []
ab1 = []
for i in range(n):
	if ab[i][0] == 0:
		ab0.append(ab[i][1])
	else:
		ab1.append(ab[i])
ab0.sort()
ab1.sort(key=lambda x: x[0] / (x[1] + 1), reverse=True)
n = len(ab1)
dp = [[10 ** 10 for i in range(31)] for j in range(n + 1)]
for i in range(n + 1):
	dp[i][0] = 0
for i in range(1, n + 1):
	(a, b) = ab1[i - 1]
	for j in range(1, 31):
		dp[i][j] = min(dp[i - 1][j], dp[i - 1][j - 1] + 1 + a * (dp[i - 1][j - 1] + 1) + b)
m = len(ab0)
ans = 0
for j in range(31):
	if dp[n][j] > t:
		continue
	anstmp = j
	ttmp = t - dp[n][j]
	i = 0
	while i <= m - 1 and ttmp >= ab0[i] + 1:
		ttmp -= ab0[i] + 1
		anstmp += 1
		i += 1
	ans = max(ans, anstmp)
print(ans)


def solve(n, t, ab_list):
	a0b_list = [ab[1] for ab in ab_list if ab[0] == 0]
	apb_list = [ab for ab in ab_list if ab[0] > 0]
	a0b_list = sorted(a0b_list)
	apb_list = sorted(apb_list, key=lambda x: -x[0] / (x[1] + 1))
	m = len(apb_list)
	dp = [[t + 1] * 30 for _ in range(m + 1)]
	for i in range(m + 1):
		dp[i][0] = 0
	for i in range(m):
		for k in range(1, 30):
			ti = dp[i][k - 1] + 1
			(a, b) = apb_list[i]
			dp[i + 1][k] = min(dp[i][k], ti + a * ti + b)
	a0b_list_cum_sum = [0]
	s = 0
	for b in a0b_list:
		s += b + 1
		a0b_list_cum_sum.append(s)
	res = 0
	for k in range(len(a0b_list_cum_sum)):
		for p in range(30):
			if dp[m][p] + a0b_list_cum_sum[k] <= t:
				res = max(res, k + p)
	return res

def main():
	(n, t) = map(int, input().split())
	ab_list = [list(map(int, input().split())) for _ in range(n)]
	res = solve(n, t, ab_list)
	print(res)

def test():
	assert solve(3, 7, [[2, 0], [3, 2], [0, 3]]) == 2
	assert solve(1, 3, [[0, 3]]) == 0
	assert solve(5, 21600, [[2, 14], [3, 22], [1, 3], [1, 10], [1, 9]]) == 5
test()
main()


(N, T) = map(int, input().split())
X = []
for _ in range(N):
	(a, b) = map(int, input().split())
	X.append((a, b))
X.sort(key=lambda x: x[0] / (x[1] + 1))
X = X[::-1]
dp = [[0] + [T + 2] * 29 for _ in range(N + 1)]
bs = []
fi = 0
for (i, (a, b)) in enumerate(X):
	if a == 0:
		bs.append(b)
		continue
	for j in range(1, 30):
		dp[i + 1][j] = min(min(dp[i][j], (a + 1) * (dp[i][j - 1] + 1) + b), T + 1)
	fi = i + 1
bs.sort()
bbs = [0]
for (i, b) in enumerate(bs):
	bbs.append(bbs[-1] + bs[i] + 1)
bbs.append(10 ** 18)
r = 0
for i in range(30):
	if dp[fi][i] > T:
		break
	nt = T - dp[fi][i]
	for (j, b) in enumerate(bbs):
		if b > nt:
			break
	r = max(r, i + j - 1)
print(r)


import sys
from bisect import bisect
from itertools import accumulate
(n, t) = map(int, input().split())
constant = []
variable = []
for line in sys.stdin:
	(a, b) = map(int, line.split())
	if a == 0:
		constant.append(b + 1)
	else:
		variable.append((a / (b + 1), a, b))
constant.sort()
variable.sort(reverse=True)
INF = 10 ** 10
t += 1
t2 = t.bit_length() + 1
dp = [INF] * t2
dp[0] = 1
for (_, a, b) in variable:
	for j in range(t2 - 1, -1, -1):
		if dp[j] == INF:
			continue
		tmp = (a + 1) * dp[j] + b + 1
		if tmp > t:
			continue
		if dp[j + 1] > tmp:
			dp[j + 1] = tmp
const_acc = list(accumulate(constant))
ans = 0
for (i, c) in enumerate(dp):
	if c == INF:
		break
	remaining = t - c
	k = bisect(const_acc, remaining)
	ans = max(ans, i + k)
print(ans)


import bisect
import sys
input = sys.stdin.readline
(N, T) = list(map(int, input().split()))
AB = [list(map(int, input().split())) for _ in range(N)]
a0 = []
nab = []
for (a, b) in AB:
	if a == 0:
		a0.append(b)
	else:
		nab.append(((b + 1) / a, a, b))
a0.sort()
nab.sort()
a0sum = []
_sum = 0
for b in a0:
	_sum += 1 + b
	a0sum.append(_sum)
INF = 1 << 32
dp = [0] + [INF] * 29
for (index, (_, a, b)) in enumerate(nab):
	ndp = [0] + [INF] * 29
	for count in range(1, 29):
		ndp[count] = min(dp[count], dp[count - 1] + 1 + (dp[count - 1] + 1) * a + b)
	dp = ndp
ans = 0
for (count, t) in enumerate(dp):
	if t > T:
		continue
	v = bisect.bisect_right(a0sum, T - t)
	ans = max(ans, v + count)
print(ans)


import sys
sys.setrecursionlimit(2147483647)
INF = 1 << 60
MOD = 10 ** 9 + 7
input = lambda : sys.stdin.readline().rstrip()
from bisect import bisect_right
from itertools import accumulate
from functools import cmp_to_key

def cmp(store1, store2):
	if store1 == store2:
		return 0
	(a1, b1) = store1
	(a2, b2) = store2
	return -1 if a2 * (b1 + 1) <= a1 * (b2 + 1) else 1

def resolve():
	(n, T) = map(int, input().split())
	AB = []
	zero = []
	for _ in range(n):
		(a, b) = map(int, input().split())
		if a != 0:
			AB.append((a, b))
		else:
			zero.append(b + 1)
	AB.sort(key=cmp_to_key(cmp))
	zero.sort()
	zero = list(accumulate(zero))
	max_store = 30
	dp = [T + 1] * max_store
	dp[0] = 0
	for (a, b) in AB:
		for i in range(max_store - 2, -1, -1):
			t = dp[i]
			dp[i + 1] = min(dp[i + 1], (a + 1) * (t + 1) + b)
	res = 0
	for i in range(max_store):
		t = dp[i]
		if t > T:
			break
		rest = T - t
		res = max(res, i + bisect_right(zero, rest))
	print(res)
resolve()


def main():
	import itertools
	import sys
	buf = sys.stdin.buffer
	(n, t) = map(int, buf.readline().split())
	m = map(int, buf.read().split())
	shops = []
	shopsA0 = [0]
	for (a, b) in zip(m, m):
		if a == 0:
			shopsA0.append(b + 1)
		else:
			shops.append([a, b])
	shopsA0.sort()
	shops.sort(reverse=True, key=lambda x: x[0] / (x[1] + 1))
	DP = [t + 10] * 30
	DP[0] = 0
	for (a, b) in shops:
		for num in range(28, -1, -1):
			candidate = (DP[num] + 1) * (a + 1) + b
			if candidate < DP[num + 1]:
				DP[num + 1] = candidate
	cumA0 = list(itertools.accumulate(shopsA0))
	ans = [0]
	count_A = 28
	for (count, spend_time) in enumerate(cumA0):
		residue = t - spend_time
		if residue < 0:
			break
		while DP[count_A] > residue:
			count_A -= 1
		ans.append(count_A + count)
	print(max(ans))
main()


def main():
	import sys
	input = sys.stdin.readline
	inf = 1 << 30
	L = 30
	(N, T) = map(int, input().split())
	ps = []
	coef_0 = []
	for _ in range(N):
		(a, b) = map(int, input().split())
		if a == 0:
			coef_0.append(b + 1)
		else:
			ps.append((a, b))
	ps.sort(key=lambda p: p[0] / (p[1] + 1), reverse=True)
	coef_0.sort()
	dp = [inf] * (L + 1)
	dp[0] = 0
	for (coef, const) in ps:
		for visited in reversed(range(L)):
			dp[visited + 1] = min(dp[visited + 1], (dp[visited] + 1) * (coef + 1) + const)

	def accumulate(a):
		s = 0
		yield s
		for x in a:
			s += x
			yield s
	(*acc,) = accumulate(coef_0)
	ans = {0}
	cnt = len(acc) - 1
	for (visited, consumption_time) in enumerate(dp):
		rest = T - consumption_time
		if rest < 0:
			break
		while cnt > 0 and acc[cnt] > rest:
			cnt -= 1
		ans.add(visited + cnt)
	print(max(ans))
main()


from bisect import bisect_right
import sys
sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline
(n, t) = map(int, input().split())
shop = []
shop_a0 = []
for i in range(n):
	(a, b) = map(int, input().split())
	if a != 0:
		shop.append([a, b, a / (b + 1)])
	else:
		shop_a0.append(b)
shop = sorted(shop, key=lambda x: -x[2])
shop_a0 = sorted(shop_a0)
n = len(shop)
INF = 10 ** 10
dp = [[INF for _ in range(31)] for __ in range(n + 1)]
dp[0][0] = 0
m = min(n + 1, 30)
for i in range(n):
	for j in range(m):
		if (shop[i][0] + 1) * (dp[i][j] + 1) + shop[i][1] > t:
			dp[i + 1][j + 1] = dp[i][j + 1]
		else:
			dp[i + 1][j + 1] = min(dp[i][j + 1], (shop[i][0] + 1) * (dp[i][j] + 1) + shop[i][1])
		dp[i + 1][j] = min(dp[i + 1][j], dp[i][j])
ss = []
if shop_a0:
	ss.append(1 + shop_a0[0])
	for i in range(1, len(shop_a0)):
		ss.append(ss[-1] + 1 + shop_a0[i])
ans = 0
for i in range(m):
	if t - dp[n][i] >= 0:
		ans = max(ans, bisect_right(ss, t - dp[n][i]) + i)
print(ans)


import sys
input = sys.stdin.readline
(n, t) = map(int, input().split())
shop = []
shop_0 = []
for i in range(n):
	(a, b) = map(int, input().split())
	if a == 0:
		shop_0.append((a, b))
		n -= 1
	else:
		shop.append((a, b))
shop.sort(key=lambda x: x[0] / (1 + x[1]), reverse=True)
shop_0.sort()
inf = 10 ** 18
dp = [[inf for i in range(30)] for j in range(n + 1)]
dp[0][0] = 0
for i in range(n):
	for j in range(29):
		dp[i + 1][j] = min(dp[i][j], dp[i + 1][j])
		dp[i + 1][j + 1] = min(dp[i + 1][j + 1], dp[i][j] + (dp[i][j] + 1) * shop[i][0] + shop[i][1] + 1)
ans = 0
for i in range(30):
	tmp = i
	T = dp[n][i]
	if T > t:
		continue
	else:
		for j in range(len(shop_0)):
			if T + shop_0[j][1] + 1 <= t:
				T += shop_0[j][1] + 1
				tmp += 1
			else:
				break
	ans = max(tmp, ans)
print(ans)


import sys
sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep='\n')

def II():
	return int(sys.stdin.readline())

def MI():
	return map(int, sys.stdin.readline().split())

def LI():
	return list(map(int, sys.stdin.readline().split()))

def LLI(rows_number):
	return [LI() for _ in range(rows_number)]

def SI():
	return sys.stdin.readline()[:-1]

class Store:

	def __init__(self, a, b):
		self.a = a
		self.b = b

	def __eq__(self, other):
		return (self.b + 1) * other.a == self.a * (other.b + 1)

	def __lt__(self, other):
		return (self.b + 1) * other.a < self.a * (other.b + 1)

	def __le__(self, other):
		return (self.b + 1) * other.a <= self.a * (other.b + 1)

	def __gt__(self, other):
		return (self.b + 1) * other.a > self.a * (other.b + 1)

	def __ge__(self, other):
		return (self.b + 1) * other.a >= self.a * (other.b + 1)
from itertools import accumulate
from bisect import bisect

def main():
	inf = 10 ** 9 + 7
	(n, t) = MI()
	ab = LLI(n)
	ss = []
	a0 = []
	for (a, b) in ab:
		if a == 0:
			a0.append(b + 1)
		else:
			ss.append(Store(a, b))
	n = len(ss)
	ss.sort()
	dp = [[inf] * 31 for _ in range(n + 1)]
	dp[0][0] = 0
	for (i, s) in enumerate(ss):
		(a, b) = (s.a, s.b)
		for j in range(30):
			pre = dp[i][j]
			if pre == inf:
				continue
			nt = a * (pre + 1) + b + pre + 1
			if nt <= t:
				dp[i + 1][j + 1] = min(dp[i + 1][j + 1], nt)
			dp[i + 1][j] = min(dp[i + 1][j], pre)
	a0.sort()
	a0 = [b for b in accumulate(a0)]
	ans = 0
	for j in range(30):
		val = dp[n][j]
		if val == inf:
			continue
		ans = max(ans, bisect(a0, t - dp[n][j]) + j)
	print(ans)
main()


import sys
from bisect import bisect_right
(N, T) = map(int, input().split())
ab = [list(map(int, input().split())) for _ in range(N)]
b0 = []
ab1 = []
for (a, b) in ab:
	if a == 0:
		b0.append(b + 1)
	else:
		ab1.append([(b + 1) / a, a, b])
N0 = len(b0)
N1 = len(ab1)
b0.sort()
if N0 > 0:
	b_ruiseki = [0] * N0
	b_ruiseki[0] = b0[0]
	for i in range(1, N0):
		b_ruiseki[i] = b_ruiseki[i - 1] + b0[i]
else:
	b_ruiseki = []
ab1.sort()
INF = T + 100
dp = [[INF] * 31 for _ in range(N1 + 1)]
dp[0][0] = 0
ans = 0
for i in range(N1):
	for j in range(31):
		if j > i + 1:
			break
		if j == 0:
			dp[i + 1][j] = 0
		else:
			dp[i + 1][j] = min(dp[i][j], (dp[i][j - 1] + 1) * (ab1[i][1] + 1) + ab1[i][2])
for j in range(31):
	if dp[N1][j] > T:
		break
	num0 = bisect_right(b_ruiseki, T - dp[N1][j])
	ans = max(ans, j + num0)
print(ans)


from operator import itemgetter
import bisect
(n, t) = map(int, input().split())
info = [list(map(int, input().split())) for i in range(n)]
INF = t + 1
LIMIT = 60
mrkt_a0 = []
mrkt_others = []
for i in range(n):
	(a, b) = info[i]
	if a == 0:
		mrkt_a0.append((a, b))
	else:
		comp = a / (1 + b)
		mrkt_others.append((a, b, comp))
mrkt_a0.sort(key=itemgetter(1))
mrkt_others.sort(key=itemgetter(2), reverse=True)
times_a0 = [0]
for (a, b) in mrkt_a0:
	times_a0.append(times_a0[-1] + 1 + b)
len_others = len(mrkt_others)
dp = [[INF] * LIMIT for i in range(len_others + 1)]
dp[0][0] = 0
for i in range(len_others):
	(a, b, _) = mrkt_others[i]
	for cnt in range(LIMIT):
		dp[i + 1][cnt] = min(dp[i][cnt], dp[i + 1][cnt])
		if cnt + 1 < LIMIT:
			dp[i + 1][cnt + 1] = min(a * (dp[i][cnt] + 1) + b + dp[i][cnt] + 1, dp[i + 1][cnt + 1])
ans = 0
for cnt in range(LIMIT):
	if dp[-1][cnt] == t + 1:
		continue
	nokori = t - dp[-1][cnt]
	cnt_a0 = bisect.bisect_right(times_a0, nokori) - 1
	ans = max(ans, cnt + cnt_a0)
print(ans)


import sys
input = sys.stdin.readline

def main():
	(N, T) = map(int, input().split())
	(a, b) = ([], [])
	a0_b = []
	for i in range(N):
		(a_in, b_in) = map(int, input().split())
		if a_in == 0:
			a0_b.append(b_in)
		else:
			a.append(a_in)
			b.append(b_in)
	L = len(a)
	ab_ratio = [a[i] / (b[i] + 1) for i in range(L)]
	key = sorted(range(L), key=lambda x: -ab_ratio[x])
	a = [a[i] for i in key]
	b = [b[i] for i in key]
	a0_b.sort()
	J_MAX = min(L + 1, 29)
	dp = [[float('inf') for _ in range(J_MAX)] for _ in range(L + 1)]
	dp[0][0] = 0
	for i in range(L):
		for j in range(J_MAX):
			if j > 0:
				dt = 1 + a[i] * (dp[i][j - 1] + 1) + b[i]
				if dp[i][j - 1] + dt <= T:
					dp[i + 1][j] = min(dp[i][j], dp[i][j - 1] + dt)
				else:
					dp[i + 1][j] = dp[i][j]
			else:
				dp[i + 1][j] = dp[i][j]
	ans = 0
	for i in range(J_MAX):
		if dp[L][i] == float('inf'):
			break
		else:
			time_cnt = dp[L][i]
			shop_cnt = i
			for t_b in a0_b:
				if time_cnt + 1 + t_b <= T:
					time_cnt += 1 + t_b
					shop_cnt += 1
			if ans < shop_cnt:
				ans = shop_cnt
	print(ans)
main()


def examA():
	S = SI()
	if len(S) % 2 == 1:
		print('No')
		return
	for i in range(len(S) // 2):
		if S[i * 2:i * 2 + 2] != 'hi':
			print('No')
			return
	print('Yes')
	return

def examB():
	(a, b, M) = LI()
	A = LI()
	B = LI()
	D = [LI() for _ in range(M)]
	ans = min(A) + min(B)
	for (x, y, c) in D:
		cur = A[x - 1] + B[y - 1] - c
		ans = min(ans, cur)
	print(ans)
	return

def examC():

	def bfs(n, e, fordfs):
		W = [-1] * n
		W[e] = 0
		que = deque()
		que.append(e)
		while que:
			now = que.popleft()
			nowW = W[now]
			for ne in fordfs[now]:
				if W[ne] == -1:
					W[ne] = nowW + 1
					que.append(ne)
		return W
	N = I()
	V = [[] for _ in range(N)]
	for _ in range(N - 1):
		(a, b) = LI()
		a -= 1
		b -= 1
		V[a].append(b)
		V[b].append(a)
	L = bfs(N, 0, V)
	odd = 0
	for l in L:
		if l == -1:
			print(-1)
			return
		if l % 2 == 1:
			odd += 1
	G = []
	if odd * 2 < N:
		for i in range(N):
			if L[i] % 2 == 1:
				G.append(i)
	else:
		for i in range(N):
			if L[i] % 2 == 0:
				G.append(i)
	used = [False] * (N + 1)
	ans = [0] * N
	if N // 3 >= len(G):
		cur = 3
		for g in G:
			ans[g] = cur
			used[cur] = True
			cur += 3
		cur = 1
		for i in range(N):
			if ans[i] != 0:
				continue
			while used[cur]:
				cur += 1
			ans[i] = cur
			used[cur] = True
	else:
		cur = 1
		for g in G:
			ans[g] = cur
			used[cur] = True
			cur += 3
			if cur > N:
				cur = 3
		cur = 1
		for i in range(N):
			if ans[i] != 0:
				continue
			while used[cur]:
				cur += 1
			ans[i] = cur
			used[cur] = True
	print(' '.join(map(str, ans)))
	return

def examD():
	(N, T) = LI()
	A = []
	A0 = []
	for _ in range(N):
		(a, b) = LI()
		if a == 0:
			A0.append(b)
		else:
			A.append((a / (b + 1), a, b))
	A.sort(reverse=True)
	n = len(A)
	S = min(31, n)
	dp = [[inf] * (n + 1) for _ in range(S + 1)]
	dp[0][0] = 0
	for (i, (_, a, b)) in enumerate(A):
		for j in range(S):
			now = dp[j][i] + 1
			dp[j][i + 1] = min(dp[j][i + 1], dp[j][i])
			if now == inf:
				continue
			dp[j + 1][i + 1] = min(dp[j + 1][i + 1], now + a * now + b)
	dp0 = [0] * (len(A0) + 1)
	A0.sort()
	for (i, b) in enumerate(A0):
		dp0[i + 1] = dp0[i] + b + 1
	ans = 0
	for i in range(S + 1):
		t = T - min(dp[i])
		if t < 0:
			break
		cur = bisect.bisect_right(dp0, t) - 1 + i
		if ans < cur:
			ans = cur
	print(ans)
	return

def examE():
	(N, M) = LI()
	H = 2 ** N - 1
	W = 2 ** M - 1
	ans = [[0] * W for _ in range(H)]
	for h in range(H):
		flagh = False
		for m in range(1, 11)[::-1]:
			if (h + 1) % 2 ** m == 0:
				flagh = 2 ** m * 2
		for w in range(W):
			flagw = False
			for m in range(1, 11)[::-1]:
				if (w + 1) % 2 ** m == 0:
					flagw = 2 ** m * 2
			if flagh and flagw:
				continue
			ans[h][w] = 1
	for v in ans:
		print(''.join(map(str, v)))
	return

def examF():
	ans = 0
	print(ans)
	return
import sys, bisect, itertools, heapq, math, random
from copy import deepcopy
from heapq import heappop, heappush, heapify
from collections import Counter, defaultdict, deque

def I():
	return int(sys.stdin.readline())

def LI():
	return list(map(int, sys.stdin.readline().split()))

def LSI():
	return list(map(str, sys.stdin.readline().split()))

def LS():
	return sys.stdin.readline().split()

def SI():
	return sys.stdin.readline().strip()
global mod, mod2, inf, alphabet, _ep
mod = 10 ** 9 + 7
mod2 = 998244353
inf = 10 ** 18
_ep = 10 ** (-12)
alphabet = [chr(ord('a') + i) for i in range(26)]
sys.setrecursionlimit(10 ** 6)
examD()


from bisect import bisect_left
import sys
input = sys.stdin.readline
(n, t) = map(int, input().split())
ab = []
a0 = []
for i in range(n):
	(a, b) = map(int, input().split())
	if a == 0:
		a0.append(b)
	else:
		ab.append([a / (b + 1), a, b])
a0.sort()
ab.sort(reverse=True)
INF = 10 ** 12
N = 40
m = len(ab)
dp = [[INF for _ in range(N)] for _ in range(m + 1)]
dp[0][0] = 0
for i in range(1, m + 1):
	(a, b) = (ab[i - 1][1], ab[i - 1][2])
	dp[i][0] = 0
	for j in range(1, N):
		tmp = 1 + dp[i - 1][j - 1]
		dp[i][j] = min(dp[i - 1][j], tmp + (a * tmp + b))
ans = 0
for i in range(N):
	time = dp[-1][i]
	ans_tmp = i
	if time <= t:
		for v in a0:
			time += 1 + v
			if time <= t:
				ans_tmp += 1
			else:
				break
		ans = max(ans, ans_tmp)
print(ans)


import sys
sr = lambda : sys.stdin.readline().rstrip()
ir = lambda : int(sr())
lr = lambda : list(map(int, sr().split()))
from itertools import accumulate

def resolve():
	(N, T) = lr()
	ab = []
	a0b = [0]
	for i in range(N):
		(a, b) = lr()
		if a >= 1:
			ab.append([a, b])
		else:
			a0b.append(b + 1)
	ab = sorted(ab, key=lambda x: x[0] / (x[1] + 1))[::-1]
	a0b = sorted(a0b)
	dp = [T + 1] * 30
	dp[0] = 0
	for (a, b) in ab:
		for i in range(28, -1, -1):
			t = (a + 1) * (dp[i] + 1) + b
			if t < dp[i + 1]:
				dp[i + 1] = t
	ans = 0
	acc = list(accumulate(a0b))
	num = len(acc) - 1
	for i in range(30):
		t = dp[i]
		if t > T + 0.5:
			break
		while num > 0 and t + acc[num] > T + 0.5:
			num -= 1
		ans = max(ans, i + num)
	print(ans)
resolve()


import sys
import math
import itertools
import bisect
INF = int(1e+18)

def main():
	(n, t) = map(int, sys.stdin.readline().split())
	nzshops = []
	zshops = []
	for _ in range(n):
		(a, b) = map(int, sys.stdin.readline().split())
		(zshops if a == 0 else nzshops).append((a, b))
	nzshops.sort(key=lambda x: x[0] / (x[0] + x[1] + 1), reverse=True)
	zshops.sort()
	dp = [0]
	for i in range(len(nzshops)):
		dp_ = dp + [INF]
		for c in range(1, len(dp_)):
			(a, b) = nzshops[i]
			x = dp[c - 1] + 1
			dp_[c] = min(dp_[c], x + x * a + b)
		dp = [x for x in dp_ if x <= t]
	rs = list(itertools.accumulate((1 + b for (_, b) in zshops)))
	ans = max((c + bisect.bisect(rs, t - dp[c]) for c in range(len(dp)) if dp[c] <= t))
	print(ans)
main()


import sys

def input():
	return sys.stdin.buffer.readline()[:-1]
(n, T) = map(int, input().split())
zero = []
non_zero = []
for _ in range(n):
	(a, b) = map(int, input().split())
	if a == 0:
		zero.append(b)
	else:
		non_zero.append((a, b))
zero.sort()
if not zero:
	z_cum = []
else:
	z_cum = [zero[0] + 1]
	for i in range(1, len(zero)):
		z_cum.append(z_cum[-1] + zero[i] + 1)
non_zero.sort(key=lambda x: (x[1] + 1) / x[0])
l = len(non_zero)
k = min(30, l)
INF = 10 ** 10
dp = [[INF for _ in range(k + 1)] for _ in range(l + 1)]
dp[0][0] = 0
for i in range(l):
	(a, b) = non_zero[i]
	dp[i + 1][0] = 0
	for j in range(1, k + 1):
		dp[i + 1][j] = min(dp[i][j], dp[i][j - 1] + 1 + a * (dp[i][j - 1] + 1) + b)
ans = 0
cur = 0
for i in range(k, -1, -1):
	if dp[l][i] > T:
		continue
	while cur < len(z_cum) and dp[l][i] + z_cum[cur] <= T:
		cur += 1
	ans = max(ans, i + cur)
print(ans)


import sys
input = sys.stdin.readline
(N, T) = map(int, input().split())
M = [list(map(int, input().split())) for i in range(N)]

def compare(x, y):
	if x == 0:
		return (1 << 31) + y
	else:
		return (y + 1) / x
M.sort(key=lambda x: compare(x[0], x[1]))
k = N
for i in range(N):
	if M[i][0] == 0:
		k = i
		break
DP = [[T + 1] * (k + 1) for i in range(30)]
for i in range(k + 1):
	DP[0][i] = 0

def nexttime(x, a, b):
	return x + 1 + a * (x + 1) + b
for i in range(1, 30):
	for j in range(1, k + 1):
		nt = nexttime(DP[i - 1][j - 1], M[j - 1][0], M[j - 1][1])
		DP[i][j] = min(DP[i][j - 1], nt)
ANS = 0
for i in range(30):
	TIME = min(DP[i])
	if TIME > T:
		break
	SC = i
	for j in range(k, N):
		if TIME + M[j][1] + 1 <= T:
			TIME += M[j][1] + 1
			SC += 1
	ANS = max(ANS, SC)
print(ANS)


(N, T) = map(int, input().split())
shop = []
easyshop = []
for i in range(N):
	(a, b) = map(int, input().split())
	(A, B) = (a + 1, a + b + 1)
	if A == 1:
		easyshop.append(B)
	else:
		shop.append(((A - 1) / B, A, B))
shop.sort(reverse=True)
easyshop.sort()
if shop:
	dp = [0, shop[0][2]]
	for i in range(1, len(shop)):
		ndp = []
		(val, A, B) = shop[i]
		for j in range(len(dp)):
			t = min(A * dp[j - 1] + B, dp[j])
			if T >= t:
				ndp.append(t)
			else:
				break
		else:
			t = A * dp[-1] + B
			if T >= t:
				ndp.append(t)
		dp = ndp
	import bisect
	id = bisect.bisect_right(dp, T)
	ans = id - 1
	if not easyshop:
		print(ans)
	else:
		n = len(easyshop)
		for i in range(1, n):
			easyshop[i] += easyshop[i - 1]
		for i in range(n):
			if T >= easyshop[i]:
				id = bisect.bisect_right(dp, T - easyshop[i])
				ans = max(ans, id + i)
			else:
				break
		print(ans)
else:
	import bisect
	n = len(easyshop)
	for i in range(1, n):
		easyshop[i] += easyshop[i - 1]
	ans = bisect.bisect_right(easyshop, T)
	print(ans)


import sys
import math
import itertools
import bisect
INF = int(1e+18)
T_MAX = int(1000000000.0)

def main():
	(N, T) = map(int, sys.stdin.readline().split())
	shops = [tuple(map(int, sys.stdin.readline().split())) for _ in range(N)]
	nzshops = [(a, b) for (a, b) in shops if a > 0]
	zshops = [(a, b) for (a, b) in shops if a == 0]
	nzshops.sort(key=lambda x: x[0] / (x[0] + x[1] + 1), reverse=True)
	zshops.sort()
	dp = [[0] + [INF] * int(math.log(T_MAX, 2)) for _ in range(len(nzshops) + 1)]
	for i in range(1, len(dp)):
		for c in range(1, len(dp[i])):
			(a, b) = nzshops[i - 1]
			t = dp[i - 1][c - 1] + 1
			dp[i][c] = min(dp[i - 1][c], t + t * a + b)
	rs = list(itertools.accumulate((1 + b for (_, b) in zshops)))
	ans = max((c + bisect.bisect(rs, T - dp[-1][c]) for c in range(len(dp[-1])) if dp[-1][c] <= T))
	print(ans)
main()