#include <bits/stdc++.h>
using namespace std;
const long long mod = 1e9+7;
int n;
long long r1, r2, r3, wyn;
long long F[10500];
bitset <10005> B1, B2, B3;
long long NpoK(long long N, long long K)
{
long long war[10005] = {};
for (long long i = max(N-K+1, K+1); i <= N; i++)
{
long long x = i;
while (F[x] > 0)
{
war[F[x]]++;
x /= F[x];
}
}
long long lim = min(N-K, K);
for (long long i = 2; i <= lim; i++)
{
long long x = i;
while (F[x] > 0)
{
war[F[x]]--;
x /= F[x];
}
}
long long ans = 1;
for (long long i = 2; i <= N; i++)
while (war[i])
{
ans = (ans * i) % mod;
war[i]--;
}
return ans;
}
void add(long long r)
{
for (long long i = 0; i <= r; i++)
wyn = (wyn + NpoK(n, i)) % mod;
}
void sub(long long ra, bitset <10005> A, long long rb, bitset <10005> B)
{
long long dif = 0;
for (int i = 0; i < n; i++)
if (A[i] != B[i])
dif++;
long long same = n-dif;
long long ans = 0;
for (long long i = 0; i <= ra; i++)
{
for (long long j = 0; j <= rb; j++)
{
if (i+j < dif || (i+j-dif)%2)
continue;
long long poza = (i+j-dif)/2;
ans = (ans + (NpoK(dif, i-poza) * NpoK(same, poza))) % mod;
}
}
wyn = (wyn - ans + mod) % mod;
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cin >> n >> r1 >> B1 >> r2 >> B2 >> r3 >> B3;
for (int i = 2; i <= n+10; i++)
if (!F[i])
{
F[i] = i;
for (int j = i*i; j <= n; j += i)
F[j] = i;
}
add(r1);
add(r2);
add(r3);
sub(r1, B1, r2, B2);
sub(r2, B2, r3, B3);
sub(r3, B3, r1, B1);
cout << wyn << '\n';
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 | #include <bits/stdc++.h> using namespace std; const long long mod = 1e9+7; int n; long long r1, r2, r3, wyn; long long F[10500]; bitset <10005> B1, B2, B3; long long NpoK(long long N, long long K) { long long war[10005] = {}; for (long long i = max(N-K+1, K+1); i <= N; i++) { long long x = i; while (F[x] > 0) { war[F[x]]++; x /= F[x]; } } long long lim = min(N-K, K); for (long long i = 2; i <= lim; i++) { long long x = i; while (F[x] > 0) { war[F[x]]--; x /= F[x]; } } long long ans = 1; for (long long i = 2; i <= N; i++) while (war[i]) { ans = (ans * i) % mod; war[i]--; } return ans; } void add(long long r) { for (long long i = 0; i <= r; i++) wyn = (wyn + NpoK(n, i)) % mod; } void sub(long long ra, bitset <10005> A, long long rb, bitset <10005> B) { long long dif = 0; for (int i = 0; i < n; i++) if (A[i] != B[i]) dif++; long long same = n-dif; long long ans = 0; for (long long i = 0; i <= ra; i++) { for (long long j = 0; j <= rb; j++) { if (i+j < dif || (i+j-dif)%2) continue; long long poza = (i+j-dif)/2; ans = (ans + (NpoK(dif, i-poza) * NpoK(same, poza))) % mod; } } wyn = (wyn - ans + mod) % mod; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cin >> n >> r1 >> B1 >> r2 >> B2 >> r3 >> B3; for (int i = 2; i <= n+10; i++) if (!F[i]) { F[i] = i; for (int j = i*i; j <= n; j += i) F[j] = i; } add(r1); add(r2); add(r3); sub(r1, B1, r2, B2); sub(r2, B2, r3, B3); sub(r3, B3, r1, B1); cout << wyn << '\n'; } |
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