The Travelling Salesman spends a lot of time travelling so he tends to get bored. To pass time, he likes to perform operations on numbers. One such operation is to take a positive integer x and reduce it to the number of bits set to 1 in the binary representation of x. For example for number 13 it's true that 13_10 = 1101_2, so it has 3 bits set and 13 will be reduced to 3 in one operation.

He calls a number special if the minimum number of operations to reduce it to 1 is k.

He wants to find out how many special numbers exist which are not greater than n. Please help the Travelling Salesman, as he is about to reach his destination!

Since the answer can be large, output it modulo 10^9 + 7.


-----Input-----

The first line contains integer n (1 ≤ n < 2^1000).

The second line contains integer k (0 ≤ k ≤ 1000).

Note that n is given in its binary representation without any leading zeros.


-----Output-----

Output a single integer — the number of special numbers not greater than n, modulo 10^9 + 7.


-----Examples-----
Input
110
2

Output
3

Input
111111011
2

Output
169



-----Note-----

In the first sample, the three special numbers are 3, 5 and 6. They get reduced to 2 in one operation (since there are two set bits in each of 3, 5 and 6) and then to 1 in one more operation (since there is only one set bit in 2).

Difficulty: MEDIUM_HARD
Tags: Dynamic programming

Combinatorics

Complete search
Skill types: Dynamic programming

Complete search
Expected Time Complexity: O(N)

Starter code:

Solutions:
def main():
	(s, k) = (input(), int(input()))
	n = len(s)
	if k < 2:
		print((1, n - 1)[k])
		return
	tais = [n - i - 1 for (i, c) in enumerate(s) if c == '1']
	(tlen, cache, res) = (len(tais), {(0, 0): 1}, 0)

	def c(n, m):
		if n < m * 2:
			m = n - m
		if 0 <= m:
			if (n, m) not in cache:
				cache[n, m] = (c(n - 1, m - 1) + c(n - 1, m)) % 1000000007
			return cache[n, m]
		return 0
	for m in range(n, 0, -1):
		(x, t) = (m, k)
		while x != 1:
			y = 0
			t -= 1
			while x:
				y += x & 1
				x //= 2
			x = y
		if t == 1:
			if len(tais) > m:
				del tais[m:]
			res += sum((c(t, m - i) for (i, t) in enumerate(tais))) + (m <= tlen)
	print(res % 1000000007)
from sys import setrecursionlimit
setrecursionlimit(1050)
main()


N = 1030
MOD = int(1000000000.0 + 7)
c = [[0] * N for i in range(N)]
for i in range(N):
	c[i][0] = 1
for i in range(1, N):
	for j in range(1, N):
		c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % MOD
arr = list(map(int, list(input())))
cnt = int(input())
if cnt == 0:
	print(1)
	exit()
dp = [0] * N
for i in range(2, N):
	dp[i] = dp[bin(i).count('1')] + 1
res = 0
for i in range(1, N):
	if dp[i] != cnt - 1:
		continue
	(n, k) = (len(arr) - 1, i)
	for pos in range(len(arr)):
		if arr[pos] == 1:
			res = (res + c[n][k]) % MOD
			k -= 1
		n -= 1
	if n == -1 and k == 0:
		res += 1
if cnt == 1:
	res -= 1
print(res)


s0 = input()
k = int(input())
s1 = s0[::-1]
lens1 = len(s1)
maxnum = 1005
mod = 1000000007
dp = [[0] * maxnum for tmpi in range(maxnum)]
f = [0] * maxnum
c = [[0] * maxnum for tmpi in range(maxnum)]

def cntone(num):
	tmps = bin(num)[2:]
	cnt = 0
	for i in range(len(tmps)):
		if tmps[i] == '1':
			cnt += 1
	return cnt
for i in range(1, maxnum):
	if i == 1:
		f[i] = 0
	else:
		f[i] = f[cntone(i)] + 1
for i in range(maxnum):
	if i == 0:
		c[i][0] = 1
		continue
	for j in range(i + 1):
		if j == 0:
			c[i][j] = 1
		else:
			c[i][j] = (c[i - 1][j - 1] + c[i - 1][j]) % mod
for i in range(lens1):
	if i == 0:
		dp[i][0] = 1
		if s1[i] == '1':
			dp[i][1] = 1
		else:
			dp[i][1] = 0
		continue
	else:
		for j in range(0, i + 2):
			if j == 0:
				dp[i][j] = 1
				continue
			if s1[i] == '1':
				dp[i][j] = (dp[i - 1][j - 1] + c[i][j]) % mod
			else:
				dp[i][j] = dp[i - 1][j] % mod
ans = 0
for i in range(1, lens1 + 1):
	if f[i] == k - 1:
		ans = (ans + dp[lens1 - 1][i]) % mod
if k == 0:
	ans = 1
elif k == 1:
	ans -= 1
else:
	ans = ans
print(ans)


import sys
import math
from collections import defaultdict, deque
import heapq
fact = [1]
mod = 10 ** 9 + 7
for i in range(1, 1005):
	fact.append(i * fact[-1] % mod)

def comb(n, k, fact):
	x = fact[n]
	y = pow(fact[k], mod - 2, mod)
	z = pow(fact[n - k], mod - 2, mod)
	return x * (y * z) % mod

def getset(num):
	cnt = 0
	while num > 0:
		cnt += num % 2
		num = num >> 1
	return cnt

def get(s, bits):
	n = len(s)
	if n != 0 and bits == 0:
		return 1
	if n == 0 and bits == 0:
		return 1
	if n == 0:
		return 0
	if s[0] == '1':
		ans = 0
		if n - 1 >= bits:
			ans += comb(n - 1, bits, fact)
		x = get(s[1:], bits - 1)
		ans += x
		ans %= mod
		return ans
	x = get(s[1:], bits)
	x %= mod
	return x
num = sys.stdin.readline()[:-1]
m = len(num)
n = 0
for i in range(m):
	if num[i] == '1':
		n = (n << 1) + 1
	else:
		n = n << 1
k = int(sys.stdin.readline()[:-1])
if k == 0:
	print(1)
	return
dic = defaultdict(list)
for i in range(2, 1001):
	x = getset(i)
	cnt = 0
	while x != 1:
		y = getset(x)
		cnt += 1
		x = y
	dic[cnt + 1].append(i)
ans = 0
s = num
dic[0] = [1]
for j in dic[k - 1]:
	if j <= n:
		x = get(s, j)
		ans += x
		ans %= mod
if s == '1' and k == 1:
	print(0)
	return
if k == 1:
	ans -= 1
print(ans)


def reduce(n):
	n = bin(n)[2:]
	n = list(n)
	n = list(map(int, n))
	return sum(n)

def a(n, bits, dp):
	if bits == 0:
		return 1
	if n == '0' or n == '':
		return 0
	if bits > len(n):
		return 0
	if bits == len(n):
		if n == '1' * len(n):
			return 1
		else:
			return 0
	ans = 0
	while bits != 0 and (n != '' and n != '0') and (bits < len(n)):
		ans += dp[len(n) - 1][bits]
		i = 1
		while i < len(n) and n[i] == '0':
			i += 1
		n = n[i:]
		bits -= 1
	if bits == 0:
		ans += 1
	elif bits == len(n) and n == '1' * len(n):
		ans += 1
	return ans
n = input()
k = int(input())
if k > 5:
	print(0)
elif k == 0:
	print(1)
elif k == 1:
	print(len(n) - 1)
else:
	dp = []
	dp.append([0])
	for i in range(1, 1002):
		dp.append([])
		for j in range(i):
			if j == 0:
				dp[i].append(1)
			else:
				dp[i].append((dp[i - 1][j - 1] + dp[i - 1][j]) % 1000000007)
		dp[i].append(1)
	pos = []
	for i in range(1, len(n) + 1):
		count = 0
		I = i
		while i != 1:
			i = reduce(i)
			count += 1
		if count == k - 1:
			pos.append(I)
	ans = 0
	for i in pos:
		ans += a(n, i, dp)
	print(ans % 1000000007)


ll = [[1], [2, 4, 8, 16, 32, 64, 128, 256, 512], [3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58, 60, 65, 66, 68, 71, 72, 75, 77, 78, 80, 83, 85, 86, 89, 90, 92, 96, 99, 101, 102, 105, 106, 108, 113, 114, 116, 120, 129, 130, 132, 135, 136, 139, 141, 142, 144, 147, 149, 150, 153, 154, 156, 160, 163, 165, 166, 169, 170, 172, 177, 178, 180, 184, 192, 195, 197, 198, 201, 202, 204, 209, 210, 212, 216, 225, 226, 228, 232, 240, 255, 257, 258, 260, 263, 264, 267, 269, 270, 272, 275, 277, 278, 281, 282, 284, 288, 291, 293, 294, 297, 298, 300, 305, 306, 308, 312, 320, 323, 325, 326, 329, 330, 332, 337, 338, 340, 344, 353, 354, 356, 360, 368, 383, 384, 387, 389, 390, 393, 394, 396, 401, 402, 404, 408, 417, 418, 420, 424, 432, 447, 449, 450, 452, 456, 464, 479, 480, 495, 503, 507, 509, 510, 513, 514, 516, 519, 520, 523, 525, 526, 528, 531, 533, 534, 537, 538, 540, 544, 547, 549, 550, 553, 554, 556, 561, 562, 564, 568, 576, 579, 581, 582, 585, 586, 588, 593, 594, 596, 600, 609, 610, 612, 616, 624, 639, 640, 643, 645, 646, 649, 650, 652, 657, 658, 660, 664, 673, 674, 676, 680, 688, 703, 705, 706, 708, 712, 720, 735, 736, 751, 759, 763, 765, 766, 768, 771, 773, 774, 777, 778, 780, 785, 786, 788, 792, 801, 802, 804, 808, 816, 831, 833, 834, 836, 840, 848, 863, 864, 879, 887, 891, 893, 894, 897, 898, 900, 904, 912, 927, 928, 943, 951, 955, 957, 958, 960, 975, 983, 987, 989, 990, 999], [7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 31, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59, 61, 62, 63, 67, 69, 70, 73, 74, 76, 79, 81, 82, 84, 87, 88, 91, 93, 94, 95, 97, 98, 100, 103, 104, 107, 109, 110, 111, 112, 115, 117, 118, 119, 121, 122, 123, 124, 125, 126, 131, 133, 134, 137, 138, 140, 143, 145, 146, 148, 151, 152, 155, 157, 158, 159, 161, 162, 164, 167, 168, 171, 173, 174, 175, 176, 179, 181, 182, 183, 185, 186, 187, 188, 189, 190, 193, 194, 196, 199, 200, 203, 205, 206, 207, 208, 211, 213, 214, 215, 217, 218, 219, 220, 221, 222, 224, 227, 229, 230, 231, 233, 234, 235, 236, 237, 238, 241, 242, 243, 244, 245, 246, 248, 249, 250, 252, 259, 261, 262, 265, 266, 268, 271, 273, 274, 276, 279, 280, 283, 285, 286, 287, 289, 290, 292, 295, 296, 299, 301, 302, 303, 304, 307, 309, 310, 311, 313, 314, 315, 316, 317, 318, 321, 322, 324, 327, 328, 331, 333, 334, 335, 336, 339, 341, 342, 343, 345, 346, 347, 348, 349, 350, 352, 355, 357, 358, 359, 361, 362, 363, 364, 365, 366, 369, 370, 371, 372, 373, 374, 376, 377, 378, 380, 385, 386, 388, 391, 392, 395, 397, 398, 399, 400, 403, 405, 406, 407, 409, 410, 411, 412, 413, 414, 416, 419, 421, 422, 423, 425, 426, 427, 428, 429, 430, 433, 434, 435, 436, 437, 438, 440, 441, 442, 444, 448, 451, 453, 454, 455, 457, 458, 459, 460, 461, 462, 465, 466, 467, 468, 469, 470, 472, 473, 474, 476, 481, 482, 483, 484, 485, 486, 488, 489, 490, 492, 496, 497, 498, 500, 504, 511, 515, 517, 518, 521, 522, 524, 527, 529, 530, 532, 535, 536, 539, 541, 542, 543, 545, 546, 548, 551, 552, 555, 557, 558, 559, 560, 563, 565, 566, 567, 569, 570, 571, 572, 573, 574, 577, 578, 580, 583, 584, 587, 589, 590, 591, 592, 595, 597, 598, 599, 601, 602, 603, 604, 605, 606, 608, 611, 613, 614, 615, 617, 618, 619, 620, 621, 622, 625, 626, 627, 628, 629, 630, 632, 633, 634, 636, 641, 642, 644, 647, 648, 651, 653, 654, 655, 656, 659, 661, 662, 663, 665, 666, 667, 668, 669, 670, 672, 675, 677, 678, 679, 681, 682, 683, 684, 685, 686, 689, 690, 691, 692, 693, 694, 696, 697, 698, 700, 704, 707, 709, 710, 711, 713, 714, 715, 716, 717, 718, 721, 722, 723, 724, 725, 726, 728, 729, 730, 732, 737, 738, 739, 740, 741, 742, 744, 745, 746, 748, 752, 753, 754, 756, 760, 767, 769, 770, 772, 775, 776, 779, 781, 782, 783, 784, 787, 789, 790, 791, 793, 794, 795, 796, 797, 798, 800, 803, 805, 806, 807, 809, 810, 811, 812, 813, 814, 817, 818, 819, 820, 821, 822, 824, 825, 826, 828, 832, 835, 837, 838, 839, 841, 842, 843, 844, 845, 846, 849, 850, 851, 852, 853, 854, 856, 857, 858, 860, 865, 866, 867, 868, 869, 870, 872, 873, 874, 876, 880, 881, 882, 884, 888, 895, 896, 899, 901, 902, 903, 905, 906, 907, 908, 909, 910, 913, 914, 915, 916, 917, 918, 920, 921, 922, 924, 929, 930, 931, 932, 933, 934, 936, 937, 938, 940, 944, 945, 946, 948, 952, 959, 961, 962, 963, 964, 965, 966, 968, 969, 970, 972, 976, 977, 978, 980, 984, 991, 992, 993, 994, 996, 1000], [127, 191, 223, 239, 247, 251, 253, 254, 319, 351, 367, 375, 379, 381, 382, 415, 431, 439, 443, 445, 446, 463, 471, 475, 477, 478, 487, 491, 493, 494, 499, 501, 502, 505, 506, 508, 575, 607, 623, 631, 635, 637, 638, 671, 687, 695, 699, 701, 702, 719, 727, 731, 733, 734, 743, 747, 749, 750, 755, 757, 758, 761, 762, 764, 799, 815, 823, 827, 829, 830, 847, 855, 859, 861, 862, 871, 875, 877, 878, 883, 885, 886, 889, 890, 892, 911, 919, 923, 925, 926, 935, 939, 941, 942, 947, 949, 950, 953, 954, 956, 967, 971, 973, 974, 979, 981, 982, 985, 986, 988, 995, 997, 998]]
facts = [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 227020758, 178290591, 674358851, 789741546, 425606191, 660911389, 557316307, 146326063, 72847302, 602640637, 860734560, 657629300, 440732388, 459042011, 394134213, 35757887, 36978716, 109361473, 390205642, 486580460, 57155068, 943272305, 14530444, 523095984, 354551275, 472948359, 444985875, 799434881, 776829897, 626855450, 954784168, 10503098, 472639410, 741412713, 846397273, 627068824, 726372166, 318608048, 249010336, 948537388, 272481214, 713985458, 269199917, 75195247, 286129051, 595484846, 133605669, 16340084, 996745124, 798197261, 286427093, 331333826, 536698543, 422103593, 280940535, 103956247, 172980994, 108669496, 715534167, 518459667, 847555432, 719101534, 932614679, 878715114, 661063309, 562937745, 472081547, 766523501, 88403147, 249058005, 671814275, 432398708, 753889928, 834533360, 604401816, 187359437, 674989781, 749079870, 166267694, 296627743, 586379910, 119711155, 372559648, 765725963, 275417893, 990953332, 104379182, 437918130, 229730822, 432543683, 551999041, 407899865, 829485531, 925465677, 24826746, 681288554, 260451868, 649705284, 117286020, 136034149, 371858732, 391895154, 67942395, 881317771, 114178486, 473061257, 294289191, 314702675, 79023409, 640855835, 825267159, 333127002, 640874963, 750244778, 281086141, 979025803, 294327705, 262601384, 400781066, 903100348, 112345444, 54289391, 329067736, 753211788, 190014235, 221964248, 853030262, 424235847, 817254014, 50069176, 159892119, 24464975, 547421354, 923517131, 757017312, 38561392, 745647373, 847105173, 912880234, 757794602, 942573301, 156287339, 224537377, 27830567, 369398991, 365040172, 41386942, 621910678, 127618458, 674190056, 892978365, 448450838, 994387759, 68366839, 417262036, 100021558, 903643190, 619341229, 907349424, 64099836, 89271551, 533249769, 318708924, 92770232, 420330952, 818908938, 584698880, 245797665, 489377057, 66623751, 192146349, 354927971, 661674180, 71396619, 351167662, 19519994, 689278845, 962979640, 929109959, 389110882, 98399701, 89541861, 460662776, 289903466, 110982403, 974515647, 928612402, 722479105, 218299090, 96415872, 572421883, 774063320, 682979494, 693774784, 611379287, 166890807, 880178425, 837467962, 705738750, 616613957, 338771924, 497191232, 896114138, 560652457, 661582322, 224945188, 262995829, 859081981, 857116478, 279856786, 408062844, 406076419, 367193638, 985761614, 767884817, 77737051, 801784560, 410447512, 813374614, 702909132, 777826615, 11426636, 685259446, 721228129, 931065383, 593559607, 860745086, 578819198, 495425745, 893029457, 6156532, 502193801, 37480384, 220174401, 383076669, 3013247, 750298503, 574624441, 230733683, 144887710, 656590378, 773954850, 358485371, 772254339, 469363737, 95843299, 823414273, 87709482, 892174648, 749756145, 185864756, 68295241, 98238739, 131504392, 111672419, 928208089, 687974198, 753032165, 71715287, 506557931, 290314197, 546089425, 174590825, 187067364, 817659471, 309331349, 303445769, 964814732, 112937795, 848457973, 113604679, 263728612, 162653895, 519013648, 956915940, 591788795, 26960558, 818561771, 201473695, 830318534, 283328761, 298655153, 103269519, 567777414, 629890782, 707451727, 528064896, 419467694, 259775012, 452053078, 972081682, 512829263, 412924123, 354780756, 917691336, 648929514, 519218426, 957710940, 848100261, 607279584, 78508462, 651656900, 271922065, 927371945, 976904514, 655633282, 147015495, 44958071, 431540693, 956102180, 821001984, 4640954, 508310043, 709072863, 866824584, 318461564, 773853828, 371761455, 53040744, 609526889, 972452623, 799173814, 723225821, 3874155, 305590228, 289496343, 139259591, 348260611, 756867525, 848691744, 101266155, 835557082, 267191274, 448180160, 518514435, 443022120, 614718802, 151579195, 204297074, 912569551, 137049249, 515433810, 979001276, 524451820, 229298431, 88837724, 892742699, 387369393, 840349900, 206661672, 18186411, 619853562, 246548548, 236767938, 893832644, 930410696, 321544423, 971435684, 402636244, 780681725, 194281388, 661238608, 964476271, 643075362, 439409780, 96895678, 723461710, 915447882, 785640606, 114709392, 933696835, 539582134, 739120141, 300372431, 244129985, 722433522, 26638091, 388855420, 42468156, 647517040, 474194942, 832805846, 958306874, 489519451, 339220689, 9833277, 923477502, 390998217, 790283925, 694135631, 736657340, 609563281, 873127083, 489593220, 264439147, 891171227, 489029295, 502009550, 325923608, 280525558, 857054649, 820622208, 558213940, 216997416, 487921842, 951328535, 606653379, 794417402, 449723904, 783486165, 414645478, 809681447, 114612567, 824953206, 255016498, 147060381, 88903008, 228293174, 394357308, 362355866, 900088886, 638573794, 779598451, 904922263, 451026166, 549459329, 212643744, 563246709, 391796933, 174243175, 189725986, 238337196, 60051478, 782959006, 982673239, 237607992, 685987666, 694447544, 195840153, 519748540, 446086975, 523485236, 185780714, 716004996, 214280883, 140643728, 555470704, 516522055, 116665689, 899547947, 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facts_inv = [1, 1, 500000004, 166666668, 41666667, 808333339, 301388891, 900198419, 487524805, 831947206, 283194722, 571199524, 380933296, 490841026, 320774361, 821384963, 738836565, 514049213, 639669405, 402087866, 120104394, 862862120, 130130097, 179570875, 799148792, 791965957, 761229465, 917082579, 282752951, 699405279, 123313510, 649139150, 957785605, 604781386, 958964165, 170256120, 671396008, 261389083, 243720767, 211377457, 230284438, 469031331, 654024560, 317535457, 393580354, 297635121, 202122504, 366002609, 861791727, 854322286, 57086446, 138374245, 98814890, 662241795, 956708188, 762849245, 960050886, 16842998, 379600744, 752196628, 279203279, 250478744, 971781922, 888440989, 92006891, 262953954, 367620517, 856233148, 659650492, 328400734, 261834298, 102279357, 626420551, 159266036, 785936033, 757145819, 470488764, 58058296, 590487931, 361904913, 517023815, 623666965, 775898383, 33444559, 512302915, 711909451, 833859418, 262458156, 412073391, 746203077, 108291146, 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import sys
sys.setrecursionlimit(10000)
mod = 1000000007

def combi(n, r):
	if r == 0 or r == n:
		return 1
	if r < 0 or n < r:
		return 0
	return facts[n] * facts_inv[r] % mod * facts_inv[n - r] % mod

def solve(n, m, first_time=True):
	if n == '1':
		return 1 if m == 0 or m == 1 else 0
	if m < 0 or len(n) < m:
		return 0
	if m == 0:
		return 1
	ind = n.find('1', 1)
	if ind == -1:
		if first_time:
			return combi(len(n) - 1, m) % mod
		else:
			return len(n) if m == 1 else combi(len(n) - 1, m) % mod
	else:
		if first_time and m == 1:
			return (solve(n[ind:], m - 1, False) + combi(len(n) - 1, m) - 1) % mod
		return (solve(n[ind:], m - 1, False) + combi(len(n) - 1, m)) % mod
n = input()
k = int(input())
if k > 5:
	print(0)
elif k == 0:
	print(1)
elif k == 1 and n == '1':
	print(0)
else:
	res = 0
	for m in ll[k - 1]:
		res += solve(n, m)
		res %= mod
	print(res)


import math
import heapq, bisect
import sys
from collections import deque, defaultdict
from fractions import Fraction
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 SegmentTree1:

	def __init__(self, data, default=9999999, 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 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
s = Combination(mod)

def calc(n, i):
	if i < 0:
		return 0
	ans = 0
	if i == 0:
		return 1
	if len(n) < i:
		return 0
	elif n.count('1') == 0:
		return 0
	elif n.count('0') == 0:
		if len(n) == i:
			return 1
		else:
			return s.ncr(len(n), i)
	else:
		t = 0
		one = 0
		while n[t] == '1':
			one += 1
			ans += s.ncr(len(n) - t - 1, i - t)
			ans %= mod
			t += 1
			if t == len(n):
				break
		while n[t] == '0':
			t += 1
			if t == len(n):
				break
		ans += calc(n[t:], i - one)
		return ans % mod
n = input()
k = int(input())
if k == 0:
	print(1)
	sys.exit()
tot = 0
ans = [0] * (len(n) + 1)
for i in range(2, len(n) + 1):
	ans[i] = ans[bin(i)[2:].count('1')] + 1
for i in range(1, len(n) + 1):
	if ans[i] == k - 1:
		tot = (tot + calc(n, i) % mod) % mod
if k == 1:
	if tot >= 1:
		tot -= 1
print(tot % mod)


def Numb(a, k):
	if a == 0:
		return 0
	m = len(bin(a)) - 3
	if m + 1 < k:
		return 0
	if k == 1:
		return m + 1
	if m + 1 == k:
		return Numb(a & (1 << m) - 1, k - 1)
	return C[m][k] + Numb(a & (1 << m) - 1, k - 1)
s = input()
nDec = int(s, 2)
n = len(s)
k = int(input())
C = [[1], [1, 1]]
for i in range(n):
	tmp = [1]
	for j in range(1, i + 2):
		tmp.append(C[-1][j - 1] + C[-1][j])
	tmp.append(1)
	C.append(tmp)
if k == 0:
	print(1)
else:
	NumOfOp = [0 for i in range(n + 1)]
	for i in range(2, n + 1):
		NumOfOp[i] = NumOfOp[bin(i).count('1')] + 1
	res = 0
	for i in range(1, n + 1):
		if NumOfOp[i] == k - 1:
			res += Numb(nDec, i)
	if k == 1:
		res -= 1
	print(res % (10 ** 9 + 7))


R = lambda : map(int, input().split())
mod = 10 ** 9 + 7
maxn = 1001
c = [[0 for j in range(maxn)] for i in range(maxn)]
for i in range(maxn):
	c[i][0] = 1
for i in range(1, maxn):
	for j in range(i + 1):
		c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod
arr = list(map(int, input()))
k = int(input())
if k == 0:
	print(1 if arr.count(1) else 0)
	exit(0)
ops = [0] * (maxn + 1)
ans = 0
for i in range(2, maxn):
	cnt = bin(i).count('1')
	ops[i] = ops[cnt] + 1
for i in range(1, maxn):
	if ops[i] == k - 1:
		oc = i
		for (j, x) in enumerate(arr):
			if x and oc >= 0:
				ans = (ans + c[len(arr) - j - 1][oc]) % mod
				oc -= 1
		ans = (ans + 1) % mod if arr.count(1) == i else ans
if k == 1:
	ans = (ans + mod - 1) % mod
print(ans)


mas = [[] for i in range(1001)]
mas[0].append(1)
mas[0].append(1)
for i in range(1, 1000):
	mas[i].append(1)
	for j in range(1, i):
		mas[i].append((mas[i - 1][j] + mas[i - 1][j - 1]) % (10 ** 9 + 7))
	mas[i].append(1)

def c(k, n):
	if k > n:
		return 0
	if k < 0:
		return 0
	global mas
	return mas[n][k]
m = [0] * 1000
for i in range(1, 1000):
	nw = i
	t = 0
	while nw != 1:
		nw = sum([int(j) for j in str(bin(nw)[2:])])
		t += 1
	m[i] = t
m[1] = 0
n = input()
k = int(input())
if k >= 6:
	print(0)
	exit()
if k == 0:
	print(1)
	exit()
if k == 1:
	print(len(n) - 1)
	exit()
ans = 0
for kkk in range(1, 1000):
	if m[kkk] == k - 1:
		nw = kkk
		t = 0
		for i in range(len(n)):
			if n[i] == '1':
				ans += c(nw - t, len(n) - 1 - i)
				ans %= 10 ** 9 + 7
				t += 1
		if sum([int(j) for j in n]) == kkk:
			ans += 1
			ans %= 10 ** 9 + 7
print(ans)


class Combi:

	def __init__(self, N, mod=10 ** 9 + 7):
		self.power = [1 for _ in range(N + 1)]
		self.rev = [1 for _ in range(N + 1)]
		self.mod = mod
		for i in range(2, N + 1):
			self.power[i] = self.power[i - 1] * i % self.mod
		self.rev[N] = pow(self.power[N], self.mod - 2, self.mod)
		for j in range(N, 0, -1):
			self.rev[j - 1] = self.rev[j] * j % self.mod

	def com(self, K, R):
		if not 0 <= R <= K:
			return 0
		else:
			return self.power[K] * self.rev[K - R] * self.rev[R] % self.mod

	def perm(self, K, R):
		if not 0 <= R <= K:
			return 0
		else:
			return self.power[K] * self.rev[K - R] % self.mod

def bitcnt(X):
	res = 0
	v = X
	while v:
		res += v & 1
		v >>= 1
	return res
c = Combi(10000)
NL = list(map(int, list(input())))[::-1]
N = len(NL)
K = int(input())
MOD = 10 ** 9 + 7
dp = [[0] * 1020 for i in range(1020)]
dp[0][0] = 1
for (pos, bit) in enumerate(NL):
	if bit == 1:
		for bit in range(1010):
			dp[pos + 1][bit] = (dp[pos][bit - 1] + c.com(pos, bit)) % MOD
		continue
	else:
		for bit in range(1010):
			dp[pos + 1][bit] = dp[pos][bit]
		continue
INF = 1 << 60
cnt = [INF] * 1010
cnt[1] = 0
MOD = 10 ** 9 + 7
for i in range(2, 1010):
	cnt[i] = 1 + cnt[bitcnt(i)]
if K == 0:
	print(dp[N][0])
	exit()
else:
	ans = 0
	for bitcnt in range(1010):
		if cnt[bitcnt] == K - 1:
			ans += dp[N][bitcnt]
	if K == 1:
		ans -= 1
	print(ans % MOD)
	exit()


from math import factorial
from functools import lru_cache
mod = 1000000007

def num_iters(x):
	ans = 0
	while x > 1:
		x = bin(x).count('1')
		ans += 1
	return ans

@lru_cache(maxsize=1001)
def fact(n):
	return factorial(n) % mod

def egcd(a, b):
	if a == 0:
		return (b, 0, 1)
	else:
		(g, y, x) = egcd(b % a, a)
		return (g, x - b // a * y, y)

def modinv(a, m):
	(g, x, y) = egcd(a, m)
	if g != 1:
		raise Exception('modular inverse does not exist')
	else:
		return x % m

@lru_cache(maxsize=1001)
def inv(a):
	return modinv(a, mod)

def binom(n, k):
	return fact(n) * inv(fact(k)) * inv(fact(n - k)) % mod

def num_numbers(n, i):
	ans = 0
	num_ones_in_prefix = 0
	for j in range(len(n) - 1):
		pos_right = len(n) - j - 1
		if num_ones_in_prefix + pos_right < i or num_ones_in_prefix > i:
			break
		if n[j] == '1':
			ans = (ans + binom(pos_right, i - num_ones_in_prefix)) % mod
			num_ones_in_prefix += 1
	cnt1 = n.count('1')
	if n[-1] == '0' and cnt1 == i or (n[-1] == '1' and cnt1 in (i, i + 1)):
		ans = (ans + 1) % mod
	return ans
precalc = [num_iters(x) for x in range(1001)]

def solve(n, k):
	if k == 0:
		return 1
	elif k == 1:
		return len(n) - 1
	else:
		ans = 0
		for i in range(1, 1001):
			if precalc[i] == k - 1:
				ans = (ans + num_numbers(n, i)) % mod
		return ans
n = input()
k = int(input())
print(solve(n, k))


def main():
	(s, k) = (input(), int(input()))
	n = len(s)
	if k < 2:
		print((1, n - 1)[k])
		return
	tais = [n - i - 1 for (i, c) in enumerate(s) if c == '1']
	(tlen, mod, res) = (len(tais), 1000000007, 0)
	(fac, ifac, f) = ([1], [1], 1)
	for i in range(1, n + 1):
		f = f * i % mod
		fac.append(f)
		x = v = 0
		y = u = 1
		(a, b) = (f, mod)
		while a:
			(q, r) = divmod(b, a)
			(a, b, x, y, u, v) = (r, a, u, v, x - u * q, y - v * q)
		ifac.append(x)

	def c(n, m):
		return fac[n] * ifac[m] * ifac[n - m] % mod if 0 <= m <= n else 0
	for m in range(n, 0, -1):
		(x, t) = (m, k)
		while x != 1:
			y = 0
			t -= 1
			while x:
				y += x & 1
				x //= 2
			x = y
		if t == 1:
			if len(tais) > m:
				del tais[m:]
			res += sum((c(t, m - i) for (i, t) in enumerate(tais))) + (m <= tlen)
	print(res % mod)

def __starting_point():
	main()
__starting_point()


import os, sys
from io import BytesIO, IOBase

def bit_count(x):
	ans = 0
	while x:
		x &= x - 1
		ans += 1
	return ans

def main():
	n = input().strip()
	x = len(n)
	k = int(input())
	if n == '1':
		print(int(k == 0))
		exit()
	if not k:
		print(1)
		exit()
	mod = 10 ** 9 + 7
	dp = [0] * (x + 1)
	dp[1] = 1
	for i in range(2, x + 1):
		dp[i] = dp[bit_count(i)] + 1
	dp1 = [[0] * (x + 1) for _ in range(x + 1)]
	for i in range(x + 1):
		dp1[i][0] = 1
	for i in range(1, x + 1):
		for j in range(1, i + 1):
			dp1[i][j] = (dp1[i - 1][j - 1] + dp1[i - 1][j]) % mod
	ans = 0
	cou = n.count('1')
	for i in range(1, x + 1):
		if dp[i] != k:
			continue
		se = i
		for j in range(x):
			if n[j] == '0':
				continue
			ans = (ans + dp1[x - 1 - j][se] - (se == 1 and k == 1)) % mod
			se -= 1
			if se < 0:
				break
		if cou == i:
			ans = (ans + 1) % mod
	print(ans)
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')
main()


s = input()
k = int(input())
n = len(s)
if k == 0:
	print(1)
	return
if k == 1:
	print(n - 1)
	return
st = [0, 0]
for i in range(2, 1000):
	c = 0
	for j in range(10):
		if 1 << j & i:
			c += 1
	st.append(st[c] + 1)
nums = [i for i in range(len(st)) if st[i] == k - 1 and i <= n]
if len(nums) == 0:
	print(0)
	return
max_k = nums[-1]
c = [[0 for i in range(max_k + 1)] for j in range(n + 1)]
c[0][0] = 0
for i in range(n + 1):
	c[i][0] = 0
for i in range(max_k + 1):
	c[0][i] = 0
for i in range(1, n + 1):
	c[i][1] = i
for i in range(2, n + 1):
	for j in range(2, min(i + 1, max_k + 1)):
		c[i][j] = c[i - 1][j - 1] + c[i - 1][j]
		c[i][j] %= 10 ** 9 + 7
ans = 0
for num in nums:
	cnt = num
	for i in range(n):
		if s[i] == '1':
			ans += c[n - i - 1][cnt]
			ans %= 10 ** 9 + 7
			cnt -= 1
		if cnt == 0:
			ans += 1
			break
print(ans % (10 ** 9 + 7))


dpc = [1]
dpci = []
for i in range(1, 2000):
	dpc.append(dpc[i - 1] * i % 1000000007)

def modInverse(a, m):
	m0 = m
	y = 0
	x = 1
	if m == 1:
		return 0
	while a > 1:
		q = a // m
		t = m
		m = a % m
		a = t
		t = y
		y = x - q * y
		x = t
	if x < 0:
		x = x + m0
	return x
for i in dpc:
	dpci.append(modInverse(i, 1000000007))

def c(n, r):
	if r < 0:
		return 0
	if n < r:
		return 0
	if n < 0:
		return 0
	return dpc[n] * dpci[r] * dpci[n - r]
dp = {1: 0}

def f(n):
	x = n
	b = 0
	while x != 0:
		x = x & x - 1
		b += 1
	dp[n] = dp[b] + 1
for i in range(2, 1001):
	f(i)
a = [[], [], [], [], []]
for i in dp:
	a[dp[i]].append(i)
n = input()
l = len(n)
x = []
for i in range(l):
	if n[i] == '1':
		x.append(i)
k = int(input())
if k > 5:
	print(0)
elif k == 0:
	print(1)
else:
	ans = 0
	for i in a[k - 1]:
		r = 0
		for j in x:
			if i - r < 0:
				break
			xy = c(l - j - 1, i - r)
			ans = (ans + xy) % 1000000007
			r += 1
	if len(x) in a[k - 1] and len(x) != 1:
		ans += 1
	if len(x) > 1 and k == 1:
		ans -= 1
	print(ans)


import sys
import math
input = sys.stdin.readline
from functools import cmp_to_key

def pi():
	return int(input())

def pl():
	return int(input(), 16)

def ti():
	return list(map(int, input().split()))

def ts():
	s = input()
	return list(s[:len(s) - 1])

def invr():
	return map(int, input().split())
mod = 1000000007
f = []

def fact(n, m):
	global f
	f = [1 for i in range(n + 1)]
	f[0] = 1
	for i in range(1, n + 1):
		f[i] = f[i - 1] * i % m

def fast_mod_exp(a, b, m):
	res = 1
	while b > 0:
		if b & 1:
			res = res * a % m
		a = a * a % m
		b = b >> 1
	return res

def inverseMod(n, m):
	return fast_mod_exp(n, m - 2, m)

def ncr(n, r, m):
	if n < 0 or r < 0 or r > n:
		return 0
	if r == 0:
		return 1
	return f[n] * inverseMod(f[n - r], m) % m * inverseMod(f[r], m) % m

def main():
	C()

def D():
	[n, m, k] = ti()
	w = [[] for i in range(n)]
	for i in range(n):
		w[i] = ts()
	mn = [[0 for j in range(k + 1)] for i in range(n + 1)]
	for i in range(1, n + 1):
		for j in range(k + 1):
			c = 0
			(st, en) = (-1, -1)
			for x in range(m):
				if w[i - 1][x] == '1':
					if c == j and st == -1:
						st = x
					if c < j:
						c += 1
					if c == j:
						en = x
			mn[i][j] = en - st + 1 if st != -1 and en != -1 else 0
			(st, en) = (-1, -1)
			c = 0
			for x in range(m - 1, -1, -1):
				if w[i - 1][x] == '1':
					if c == j and st == -1:
						st = x
					if c < j:
						c += 1
					if c == j:
						en = x
			if st != -1 and en != -1 >= 0:
				mn[i][j] = min(mn[i][j], st - en + 1)
	dp = [[9999999999999999 for j in range(k + 1)] for i in range(n + 1)]
	for i in range(k + 1):
		dp[0][i] = 0
	for i in range(1, n + 1):
		for j in range(k + 1):
			for x in range(k + 1):
				if j - x >= 0:
					dp[i][j] = min(dp[i][j], dp[i - 1][j - x] + mn[i][x])
	print(dp[n][k])

def getCount(n):
	x = 1
	count = 0
	while n > 0:
		if n & 1 == 1:
			count += 1
		n = n >> 1
	return count

def C():
	try:
		n = ts()
		k = pi()
		if k == 0:
			print(1)
			return
		dp = [0 for i in range(1010)]
		for i in range(1010):
			if i == 0 or i == 1:
				continue
			dp[i] = dp[getCount(i)] + 1
		fact(1010, mod)
		ans = 0
		s = n
		count = 0
		for i in range(len(s)):
			if s[i] == '0':
				continue
			for j in range(max(count, 1), 1010):
				if dp[j] == k - 1:
					ans = (ans + ncr(len(s) - i - 1, j - count, mod)) % mod
					if i == 0 and k == 1:
						ans = (ans + mod - 1) % mod
			count += 1
		count = 0
		for i in range(len(s)):
			if s[i] == '1':
				count += 1
		if dp[count] == k - 1:
			ans = (ans + 1) % mod
		print(ans)
	except:
		print(sys.exc_info()[0])
main()


import sys
from functools import reduce

def debug(*args):
	return
	print('debug ', end='')
	for x in args:
		print(x, end=' ')
	print('')
n = input()
k = int(input())
mod = 1000000007
a = [0] * 1001

def bitnum(x):
	ans = 0
	while x:
		if x & 1:
			ans += 1
		x >>= 1
	return ans
for i in range(1, 1001):
	bn = bitnum(i)
	a[i] = a[bn] + 1
a = [i for i in range(len(a)) if a[i] == k]
a = list(filter(lambda x: x <= len(n), a))
C = [None for i in range(1001)]
C[0] = [1, 0]
for i in range(1, len(C)):
	C[i] = [1] + [(C[i - 1][j] + C[i - 1][j - 1]) % mod for j in range(1, i)] + [1]
answer = 0

def cal2(x, arr):
	global answer
	while True:
		ln = len(arr)
		if x == 0:
			answer += 1
			return
		if x > ln:
			return
		if x == ln:
			if '0' in arr:
				return
			else:
				answer += 1
				return
		answer += C[ln - 1][x]
		answer %= mod
		i = arr.find('1', arr.index('1') + 1)
		if i < 0:
			if x == 1:
				answer += 1
			return
		x -= 1
		arr = arr[i:]

def cal(x):
	global answer
	answer = 0
	cal2(x, n)
	debug(answer)
	return answer % mod

def solve():
	if k == 0:
		return 1
	if len(a) == 0:
		return 0
	tmp = map(cal, a)
	debug(list(tmp))
	ans = reduce(lambda x, y: (x + y) % mod, map(cal, a))
	return ans if k != 1 else ans - 1
try:
	print(solve())
except Exception as e:
	print(k, n[-30:])


def fact(n):
	if n == 0:
		return 1
	return n * fact(n - 1)
mod = 1000000007
ncrtable = [[0 for i in range(1001)] for j in range(1001)]
ncrtable[0][0] = 1
for row in range(1, 1001):
	for col in range(row + 1):
		if col == 0:
			ncrtable[row][col] = 1
		else:
			ncrtable[row][col] = ncrtable[row - 1][col] + ncrtable[row - 1][col - 1]

def ncr(n, r):
	if n < r:
		return 0
	if r < 0:
		return 0
	return ncrtable[n][r]

def compute(n, x):
	tot = 0
	y = x
	for i in range(1000, -1, -1):
		if 1 << i & n:
			tot += ncr(i, x) % mod
			tot %= mod
			x -= 1
	if x == 0:
		return (tot + 1) % mod
	return tot % mod
arr = [0 for i in range(1002)]
arr[1] = 1
for i in range(2, 1001):
	ct = 0
	for j in range(32, -1, -1):
		if 1 << j & i:
			ct += 1
	arr[i] = arr[ct] + 1
n = int(input(), 2)
k = int(input())
ans = 0
for i in range(0, 1001):
	if arr[i] == k:
		ans = compute(n, i) + ans
		ans %= mod
if k == 1:
	ans -= 1
print(ans)
exit(0)
if n >= 1001:
	for i in range(0, 1001):
		if arr[i] == k - 1:
			ans = compute(n, i) + ans
			ans %= mod
if k != 1:
	print(ans)
else:
	print(ans - 1)


MOD = 1000000007
OBRAT = [-1] * 2000
CC = {}
FACT = [-1] * 2000
OBRAT_FACT = [-1] * 2000

def obrat(k):
	if OBRAT[k] == -1:
		OBRAT[k] = fast_pow(k, MOD - 2)
	return OBRAT[k]

def c(n, k):
	if (n, k) in CC:
		return CC[n, k]
	res = fact(n)
	res = res * obrat_fact(k) % MOD
	res = res * obrat_fact(n - k) % MOD
	CC[n, k] = res
	return res

def obrat_fact(k):
	if OBRAT_FACT[k] != -1:
		return OBRAT_FACT[k]
	res = 1
	for i in range(2, k + 1):
		res = res * obrat(i) % MOD
	OBRAT_FACT[k] = res
	return res

def fact(n):
	if FACT[n] != -1:
		return FACT[n]
	res = 1
	for i in range(2, n + 1):
		res = res * i % MOD
	FACT[n] = res
	return res

def fast_pow(x, y):
	if y == 0:
		return 1
	p = fast_pow(x, y // 2) % MOD
	p = p * p % MOD
	if y % 2:
		p = p * x % MOD
	return p
s = input()
k = int(input())
n = len(s)
if k == 1:
	print(n - 1)
	exit()
if k == 0:
	print(1)
	exit()
moves = [0] * 1025
moves[1] = 0
for i in range(2, 1024):
	ii = i
	ones = 0
	while ii > 0:
		if ii % 2 == 1:
			ones += 1
		ii //= 2
	moves[i] = moves[ones] + 1
if n < 10:
	d = 1
	a = 0
	for i in range(n - 1, -1, -1):
		a += d * int(s[i])
		d *= 2
	res = 0
	for i in range(2, a + 1):
		if moves[i] == k:
			res += 1
	print(res)
	exit()
res = 0
if moves[s.count('1')] == k - 1:
	res += 1
for i in range(1, 1024):
	ki = moves[i]
	if ki != k - 1:
		continue
	m = n - 1
	j = 0
	while m >= i and i >= 0 and (m >= 0):
		res = (res + c(m, i)) % MOD
		i -= 1
		j += 1
		while j < n and s[j] != '1':
			j += 1
		m = n - 1 - j
print(res)


n = input()
k = int(input())
MOD = int(1000000000.0 + 7)
a = {0: 0, 1: 0, 2: 1}
for i in range(3, 1001):
	s = bin(i)[2:]
	ones_count = 0
	for x in s:
		if x == '1':
			ones_count += 1
	a[i] = a[ones_count] + 1
answer = 0
table = {}

def bin_coeff(N, K):
	if K > N:
		raise Exception
	if K > N // 2:
		K = N - K
	if K == 0:
		table[N, 0] = 1
		return 1
	if (N, K) not in table:
		table[N, K] = N * bin_coeff(N - 1, K - 1) // K
	return table[N, K]
ones = 0
for (i, x) in enumerate(n):
	if x == '1':
		good = []
		N = len(n) - i - 1
		min = 0 if i > 0 else 1
		for j in range(min, N + 1):
			if a[j + ones] == k - 1:
				good.append(j)
		for x in good:
			answer = (answer + bin_coeff(N, x)) % MOD
			if i == 0 and x == 1:
				answer -= 1
		ones += 1
if a[ones] == k - 1:
	answer += 1
if k == 0:
	answer = 1
if k == 1:
	answer = len(n) - 1
answer = int(answer)
print(answer)


def count_oper(x):
	if x == 1:
		return 0
	res = 0
	y = x
	while y > 0:
		if y % 2 == 1:
			res += 1
		y = y // 2
	return count_oper(res) + 1

def solve(s, k):
	a = []
	ones = []
	for i in range(len(s)):
		c = s[i]
		a.append(int(c == '1'))
		if c == '1':
			ones.append(i)
	nones = len(ones)
	n = len(a)
	if k == 0:
		print(1)
		return
	if k == 1 and n != 1:
		print(n - 1)
		return
	if n == 1:
		if k > 0:
			print(0)
		else:
			print(1)
		return
	c = []
	c.append([0] * (n + 1))
	for n1 in range(1, n + 1):
		tmp = [0] * (n + 1)
		for m in range(n1 + 1):
			if m == 0 or m == n1:
				tmp[m] = 1
			else:
				tmp[m] = (c[n1 - 1][m - 1] + c[n1 - 1][m]) % modulo
		c.append(tmp)
	ans = 0
	for m in range(1, n + 1):
		if count_oper(m) == k - 1:
			for j in range(min(nones, m)):
				ans += c[n - ones[j] - 1][m - j] % modulo
			if nones >= m:
				ans += 1
	print(ans % modulo)
s = input()
k = int(input())
modulo = 10 ** 9 + 7
solve(s, k)


mod = 10 ** 9 + 7

def solve(n: str, k: int):
	out = 0
	if k == 0:
		out = 1
	elif k == 1:
		out = len(n) - 1
	elif k == 2:
		for i in range(1, min(len(n), 10)):
			x = 2 ** i
			cnt = 0
			for j in range(len(n)):
				if n[j] == '1':
					out += C(len(n) - j - 1, x - cnt)
					out %= mod
					cnt += 1
			if n.count('1') == x:
				out += 1
	elif 3 <= k <= 5:
		d = dict()
		cnt = 0
		for i in range(len(n)):
			if n[i] == '1':
				m = 1
				for j in range(len(n) - i):
					assertadd(d, j + cnt, m)
					m *= len(n) - i - j - 1
					m //= j + 1
				cnt += 1
		assertadd(d, n.count('1'), 1)
		for key in d:
			out += d[key] * recur(key, k - 1)
		out %= mod
	elif k >= 6:
		out = 0
	return out

def assertadd(d: dict, k, v):
	try:
		d[k] += v
	except:
		d[k] = v

def recur(k, level):
	for i in range(level):
		k = bin(k)[2:].count('1')
		if k == 1 and i != level - 1:
			return 0
	return 1 if k == 1 else 0

def C(n, k):
	if k < 0 or k > n:
		return 0
	out = 1
	for i in range(k):
		out *= n - i
		out //= i + 1
	return out % mod
n = input()
k = int(input())
print(solve(n, k))


MX = 1030
M = 1000 * 1000 * 1000 + 7
c = [[0] * MX for i in range(MX)]
for i in range(MX):
	c[i][0] = 1
for i in range(1, MX):
	for j in range(1, MX):
		c[i][j] = c[i - 1][j] + c[i - 1][j - 1]
		c[i][j] %= M
num = list(map(int, list(input())))
cnt = int(input())
dp = [0] * MX
for i in range(2, MX):
	dp[i] = dp[bin(i).count('1')] + 1
if cnt == 0:
	print(1)
	return
res = 0
for i in range(1, MX):
	if dp[i] != cnt - 1:
		continue
	n = len(num) - 1
	k = i
	for pos in range(len(num)):
		if num[pos] == 1:
			res += c[n][k]
			res %= M
			k -= 1
		n -= 1
	if n == -1 and k == 0:
		res += 1
if cnt == 1:
	res -= 1
print(res)


import os, sys
from io import BytesIO, IOBase

def bit_count(x):
	ans = 0
	while x:
		x &= x - 1
		ans += 1
	return ans

def main():
	n = input().strip()
	x = len(n)
	k = int(input())
	if n == '1':
		print(int(k == 0))
		exit()
	if not k:
		print(1)
		exit()
	mod = 10 ** 9 + 7
	dp = [0] * (x + 1)
	dp[1] = 1
	for i in range(2, x + 1):
		dp[i] = dp[bit_count(i)] + 1
	dp1 = [[0] * (x + 1) for _ in range(x + 1)]
	for i in range(x + 1):
		dp1[i][0] = 1
	for i in range(1, x + 1):
		for j in range(1, i + 1):
			dp1[i][j] = (dp1[i - 1][j - 1] + dp1[i - 1][j]) % mod
	ans = 0
	cou = n.count('1')
	for i in range(1, x + 1):
		if dp[i] != k:
			continue
		se = i
		for j in range(x):
			if n[j] == '0':
				continue
			ans = (ans + dp1[x - 1 - j][se] - (se == 1 and k == 1)) % mod
			se -= 1
			if se < 0:
				break
		if cou == i:
			ans = (ans + 1) % mod
	print(ans)
main()


import sys
from functools import lru_cache
sys.setrecursionlimit(1000000)
MOD = int(1000000000.0 + 7)

def inv(val):
	return pow(val, MOD - 2, MOD)

@lru_cache(maxsize=None)
def factorial(n):
	return 1 if n < 2 else factorial(n - 1) * n % MOD

def choose(n, k):
	return factorial(n) * inv(factorial(k) * factorial(n - k)) % MOD

def numbers_with_bits(length, n):
	nxt = 0
	res = 0
	while nxt != -1 and length > 0:
		top = len(n) - 1 - nxt
		if length <= top:
			res += choose(top, length)
			res %= MOD
		nxt = n.find('1', nxt + 1)
		length -= 1
	if length == 0:
		res += 1
	return res

def bits(n):
	return bin(n).count('1')

def solve(n, k):
	if k == 0:
		return 1
	elif k == 1:
		return len(n) - 1
	elif k > 5:
		return 0
	ans = 0
	f = [-1, 0]
	for i in range(2, 1001):
		f.append(f[bits(i)] + 1)
		if f[i] == k - 1:
			ans += numbers_with_bits(i, n)
			ans %= MOD
	return ans
print(solve(n=input(), k=int(input())))