#include<bits/stdc++.h>
using namespace std;
using i64 = long long;
char buf[1 << 23], * p1 = buf, * p2 = buf;
#define getchar() (p1==p2&&(p2=(p1=buf)+fread(buf,1,1<<21,stdin),p1==p2)?EOF:*p1++)
template<typename T> inline void re(T& x) { x = 0; T f = 1; char ch = getchar(); while (!isdigit(ch)) { if (ch == '-') f = -1; ch = getchar(); } while (isdigit(ch)) { x = x * (1 << 1) + x * (1 << 3) + (ch - 48); ch = getchar(); } x *= f; }
template<typename x, typename... y>void re(x& a, y&... b) { re(a); re(b...); }
template<typename T> inline void ps(T x) { if (x < 0) { putchar('-'); x = -x; } if (x > 9) ps(x / 10); putchar(x % 10 + '0'); }
template<typename x, typename... y>void ps(x& a, y&... b) { ps(a); putchar(' '); ps(b...); }
#define sp putchar(' ')
#define nl putchar('\n')
template<class T>
constexpr T power(T a, i64 b) {
T res = 1;
for (; b; b /= 2, a *= a) {
if (b % 2) {
res *= a;
}
}
return res;
}
constexpr i64 mul(i64 a, i64 b, i64 p) {
i64 res = a * b - i64(1.L * a * b / p) * p;
res %= p;
if (res < 0) {
res += p;
}
return res;
}
template<i64 P>
struct MLong {
i64 x;
constexpr MLong() : x{} {}
constexpr MLong(i64 x) : x{ norm(x % getMod()) } {}
static i64 Mod;
constexpr static i64 getMod() {
if (P > 0) {
return P;
}
else {
return Mod;
}
}
constexpr static void setMod(i64 Mod_) {
Mod = Mod_;
}
constexpr i64 norm(i64 x) const {
if (x < 0) {
x += getMod();
}
if (x >= getMod()) {
x -= getMod();
}
return x;
}
constexpr i64 val() const {
return x;
}
explicit constexpr operator i64() const {
return x;
}
constexpr MLong operator-() const {
MLong res;
res.x = norm(getMod() - x);
return res;
}
constexpr MLong inv() const {
assert(x != 0);
return power(*this, getMod() - 2);
}
constexpr MLong& operator*=(MLong rhs)& {
x = mul(x, rhs.x, getMod());
return *this;
}
constexpr MLong& operator+=(MLong rhs)& {
x = norm(x + rhs.x);
return *this;
}
constexpr MLong& operator-=(MLong rhs)& {
x = norm(x - rhs.x);
return *this;
}
constexpr MLong& operator/=(MLong rhs)& {
return *this *= rhs.inv();
}
friend constexpr MLong operator*(MLong lhs, MLong rhs) {
MLong res = lhs;
res *= rhs;
return res;
}
friend constexpr MLong operator+(MLong lhs, MLong rhs) {
MLong res = lhs;
res += rhs;
return res;
}
friend constexpr MLong operator-(MLong lhs, MLong rhs) {
MLong res = lhs;
res -= rhs;
return res;
}
friend constexpr MLong operator/(MLong lhs, MLong rhs) {
MLong res = lhs;
res /= rhs;
return res;
}
friend constexpr std::istream& operator>>(std::istream& is, MLong& a) {
i64 v;
is >> v;
a = MLong(v);
return is;
}
friend constexpr std::ostream& operator<<(std::ostream& os, const MLong& a) {
return os << a.val();
}
friend constexpr bool operator==(MLong lhs, MLong rhs) {
return lhs.val() == rhs.val();
}
friend constexpr bool operator!=(MLong lhs, MLong rhs) {
return lhs.val() != rhs.val();
}
};
template<>
i64 MLong<0LL>::Mod = i64(1E18) + 9;
template<int P>
struct MInt {
int x;
constexpr MInt() : x{} {}
constexpr MInt(i64 x) : x{ norm(x % getMod()) } {}
static int Mod;
constexpr static int getMod() {
if (P > 0) {
return P;
}
else {
return Mod;
}
}
constexpr static void setMod(int Mod_) {
Mod = Mod_;
}
constexpr int norm(int x) const {
if (x < 0) {
x += getMod();
}
if (x >= getMod()) {
x -= getMod();
}
return x;
}
constexpr int val() const {
return x;
}
explicit constexpr operator int() const {
return x;
}
constexpr MInt operator-() const {
MInt res;
res.x = norm(getMod() - x);
return res;
}
constexpr MInt inv() const {
assert(x != 0);
return power(*this, getMod() - 2);
}
constexpr MInt& operator*=(MInt rhs)& {
x = 1LL * x * rhs.x % getMod();
return *this;
}
constexpr MInt& operator+=(MInt rhs)& {
x = norm(x + rhs.x);
return *this;
}
constexpr MInt& operator-=(MInt rhs)& {
x = norm(x - rhs.x);
return *this;
}
constexpr MInt& operator/=(MInt rhs)& {
return *this *= rhs.inv();
}
friend constexpr MInt operator*(MInt lhs, MInt rhs) {
MInt res = lhs;
res *= rhs;
return res;
}
friend constexpr MInt operator+(MInt lhs, MInt rhs) {
MInt res = lhs;
res += rhs;
return res;
}
friend constexpr MInt operator-(MInt lhs, MInt rhs) {
MInt res = lhs;
res -= rhs;
return res;
}
friend constexpr MInt operator/(MInt lhs, MInt rhs) {
MInt res = lhs;
res /= rhs;
return res;
}
friend constexpr std::istream& operator>>(std::istream& is, MInt& a) {
i64 v;
is >> v;
a = MInt(v);
return is;
}
friend constexpr std::ostream& operator<<(std::ostream& os, const MInt& a) {
return os << a.val();
}
friend constexpr bool operator==(MInt lhs, MInt rhs) {
return lhs.val() == rhs.val();
}
friend constexpr bool operator!=(MInt lhs, MInt rhs) {
return lhs.val() != rhs.val();
}
};
template<>
int MInt<0>::Mod = 1E9 + 7;
template<int V, int P>
constexpr MInt<P> CInv = MInt<P>(V).inv();
constexpr int P = 1E9 + 7;
using Z = MInt<P>;
struct Comb {
int n;
std::vector<Z> _fac;
std::vector<Z> _invfac;
std::vector<Z> _inv;
Comb() : n{ 0 }, _fac{ 1 }, _invfac{ 1 }, _inv{ 0 } {}
Comb(int n) : Comb() {
init(n);
}
void init(int m) {
m = std::min(m, Z::getMod() - 1);
if (m <= n) return;
_fac.resize(m + 1);
_invfac.resize(m + 1);
_inv.resize(m + 1);
for (int i = n + 1; i <= m; i++) {
_fac[i] = _fac[i - 1] * i;
}
_invfac[m] = _fac[m].inv();
for (int i = m; i > n; i--) {
_invfac[i - 1] = _invfac[i] * i;
_inv[i] = _invfac[i] * _fac[i - 1];
}
n = m;
}
Z fac(int m) {
if (m > n) init(2 * m);
return _fac[m];
}
Z invfac(int m) {
if (m > n) init(2 * m);
return _invfac[m];
}
Z inv(int m) {
if (m > n) init(2 * m);
return _inv[m];
}
Z C(int n, int m) {
if (n < m || m < 0) return 0;
return fac(n) * invfac(m) * invfac(n - m);
}
Z find(int n, int m, int k) {
/* x1+x2+x3+...+xm = k and 0<=x1,x2,x3...,xm<n
x1+x2+x3+...=k+m and x1,x2,x3...xm>=1
f(i) = no of cases such that >=i numbers are >n
f(i) = m C i * (m+k-i*n-1) C (m-1)
ans= f(i) * (-1)^i for i->[0,m] */
Z ans = 0; int ops = 1;
for (int i = 0; i <= m; i++) {
Z t = C(m, i) * C(m + k - i * n - 1, m - 1);
if (ops == -1) ans -= t;
else ans += t;
ops *= -1;
}
return ans;
}
} comb;
//mod = 1E9+7
const int _N = 2010;
Z dp[2][_N];
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr); cout.tie(nullptr);
int N, A, B; re(N, A, B);
dp[1][1] = 1;
for (int i = 2; i <= N; ++i) {
int nw = i & 1, pv = (i - 1) & 1;
for (int j = 1; j <= min(i, (N + 1) >> 1); ++j) {
dp[nw][j] = 0;
if (i == A || i == B) {
dp[nw][j] += dp[pv][j] + dp[pv][j - 1];
continue;
}
dp[nw][j] += dp[pv][j - 1] * (j - (i > A) - (i > B)) + dp[pv][j + 1] * j;//不能放头，不能放尾
}
}
i64 v = dp[N & 1][1].val(); ps(v);
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
348 KB |
Output is correct |
| 2 |
Correct |
0 ms |
348 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
348 KB |
Output is correct |
| 2 |
Correct |
0 ms |
348 KB |
Output is correct |
| 3 |
Correct |
0 ms |
348 KB |
Output is correct |
| 4 |
Correct |
0 ms |
348 KB |
Output is correct |
| 5 |
Correct |
0 ms |
348 KB |
Output is correct |
| 6 |
Correct |
0 ms |
344 KB |
Output is correct |
| 7 |
Correct |
0 ms |
348 KB |
Output is correct |
| 8 |
Correct |
0 ms |
348 KB |
Output is correct |
| 9 |
Correct |
0 ms |
344 KB |
Output is correct |
| 10 |
Correct |
0 ms |
344 KB |
Output is correct |
| 11 |
Correct |
0 ms |
348 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
348 KB |
Output is correct |
| 2 |
Correct |
0 ms |
348 KB |
Output is correct |
| 3 |
Correct |
0 ms |
348 KB |
Output is correct |
| 4 |
Correct |
0 ms |
348 KB |
Output is correct |
| 5 |
Correct |
0 ms |
348 KB |
Output is correct |
| 6 |
Correct |
0 ms |
344 KB |
Output is correct |
| 7 |
Correct |
0 ms |
348 KB |
Output is correct |
| 8 |
Correct |
0 ms |
348 KB |
Output is correct |
| 9 |
Correct |
0 ms |
344 KB |
Output is correct |
| 10 |
Correct |
0 ms |
344 KB |
Output is correct |
| 11 |
Correct |
0 ms |
348 KB |
Output is correct |
| 12 |
Correct |
0 ms |
344 KB |
Output is correct |
| 13 |
Correct |
0 ms |
348 KB |
Output is correct |
| 14 |
Correct |
0 ms |
348 KB |
Output is correct |
| 15 |
Correct |
0 ms |
348 KB |
Output is correct |
| 16 |
Correct |
0 ms |
348 KB |
Output is correct |
| 17 |
Correct |
0 ms |
348 KB |
Output is correct |
| 18 |
Correct |
0 ms |
348 KB |
Output is correct |
| 19 |
Correct |
0 ms |
348 KB |
Output is correct |
| 20 |
Correct |
1 ms |
348 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
348 KB |
Output is correct |
| 2 |
Correct |
0 ms |
348 KB |
Output is correct |
| 3 |
Correct |
0 ms |
348 KB |
Output is correct |
| 4 |
Correct |
0 ms |
348 KB |
Output is correct |
| 5 |
Correct |
0 ms |
348 KB |
Output is correct |
| 6 |
Correct |
0 ms |
344 KB |
Output is correct |
| 7 |
Correct |
0 ms |
348 KB |
Output is correct |
| 8 |
Correct |
0 ms |
348 KB |
Output is correct |
| 9 |
Correct |
0 ms |
344 KB |
Output is correct |
| 10 |
Correct |
0 ms |
344 KB |
Output is correct |
| 11 |
Correct |
0 ms |
348 KB |
Output is correct |
| 12 |
Correct |
0 ms |
344 KB |
Output is correct |
| 13 |
Correct |
0 ms |
348 KB |
Output is correct |
| 14 |
Correct |
0 ms |
348 KB |
Output is correct |
| 15 |
Correct |
0 ms |
348 KB |
Output is correct |
| 16 |
Correct |
0 ms |
348 KB |
Output is correct |
| 17 |
Correct |
0 ms |
348 KB |
Output is correct |
| 18 |
Correct |
0 ms |
348 KB |
Output is correct |
| 19 |
Correct |
0 ms |
348 KB |
Output is correct |
| 20 |
Correct |
1 ms |
348 KB |
Output is correct |
| 21 |
Correct |
1 ms |
344 KB |
Output is correct |
| 22 |
Correct |
1 ms |
348 KB |
Output is correct |
| 23 |
Correct |
1 ms |
348 KB |
Output is correct |
| 24 |
Correct |
6 ms |
348 KB |
Output is correct |
| 25 |
Correct |
6 ms |
348 KB |
Output is correct |
| 26 |
Correct |
6 ms |
476 KB |
Output is correct |
| 27 |
Correct |
6 ms |
348 KB |
Output is correct |
| 28 |
Correct |
3 ms |
472 KB |
Output is correct |
