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| #include <cstdio>
#include <algorithm>
using namespace std;
template <class Type>
void read (Type &x)
{
char c;
bool flag = false;
while ((c = getchar()) < '0' || c > '9')
flag |= c == '-';
x = c - '0';
while ((c = getchar()) >= '0' && c <= '9')
x = (x << 3) + (x << 1) + c - '0';
if (flag) x = ~x + 1;
}
template <class Type, class ...Rest>
void read (Type &x, Rest &...y) { read(x); read(y...); }
template <class Type>
void write (Type x)
{
if (x < 0) putchar('-'), x = ~x + 1;
if (x > 9) write(x / 10);
putchar('0' + x % 10);
}
typedef long long LL;
const int N = 5e5 + 10, mod = 998244353;
int fact[N], ifact[N], rev[N];
int binpow (int b, int k = mod - 2)
{
int res = 1;
for (; k; k >>= 1, b = (LL)b * b % mod)
if (k & 1) res = (LL)res * b % mod;
return res;
}
void init ()
{
fact[0] = 1;
for (int i = 1; i < N; ++i)
fact[i] = (LL)fact[i - 1] * i % mod;
ifact[N - 1] = binpow(fact[N - 1]);
for (int i = N - 1; i; --i)
ifact[i - 1] = (LL)ifact[i] * i % mod;
}
void ntt (int *x, int bit, int op)
{
int tot = 1 << bit;
for (int i = 1; i < tot; ++i)
if ((rev[i] = rev[i >> 1] >> 1 | (i & 1) << bit - 1) > i)
swap(x[rev[i]], x[i]);
for (int mid = 1; mid < tot; mid <<= 1)
{
int w1 = binpow(3, (mod - 1) / (mid << 1));
if (!~op) w1 = binpow(w1);
for (int i = 0; i < tot; i += mid << 1)
for (int j = 0, k = 1; j < mid; ++j, k = (LL)k * w1 % mod)
{
int p = x[i | j], q = (LL)k * x[i | j | mid] % mod;
x[i | j] = ((LL)p + q) % mod, x[i | j | mid] = ((LL)p - q) % mod;
}
}
if (~op) return;
int itot = binpow(tot);
for (int i = 0; i < tot; ++i)
x[i] = (LL)x[i] * itot % mod;
}
void PolyMul (int n, int *f, int m, int *g, int *res)
{
int bit = 0;
while (1 << bit < n + m - 1) ++bit;
int tot = 1 << bit;
for (int i = n; i < tot; ++i) f[i] = 0;
for (int i = m; i < tot; ++i) g[i] = 0;
ntt(f, bit, 1), ntt(g, bit, 1);
for (int i = 0; i < tot; ++i)
res[i] = (LL)f[i] * g[i] % mod;
ntt(res, bit, -1);
}
void PolyMove (int *x, int len, int k)
{
static int A[N], B[N];
for (int i = 0, t = 1; i < len; ++i, t = (LL)t * k % mod)
A[len - 1 - i] = (LL)t * ifact[i] % mod;
for (int i = 0; i < len; ++i)
B[i] = (LL)fact[i] * x[i] % mod;
PolyMul(len, A, len, B, x);
for (int i = 0; i < len; ++i)
x[i] = (LL)x[len - 1 + i] * ifact[i] % mod;
}
void solve (int n, int *f)
{
if (!n) return void(f[0] = 1);
int m = n >> 1;
solve(m, f);
static int g[N];
for (int i = 0; i <= m; ++i) g[i] = f[i];
PolyMove(g, m + 1, m);
PolyMul(m + 1, f, m + 1, g, f);
if (n & 1) for (int i = n; ~i; --i)
f[i] = ((LL)(n - 1) * f[i] + (i ? f[i - 1] : 0)) % mod;
}
int main ()
{
init();
int n, A, B;
read(n, A, B);
static int res[N];
solve(n - 1, res);
write(((LL)res[A + B - 2] * fact[A + B - 2] % mod * ifact[A - 1] % mod * ifact[B - 1] % mod + mod) % mod);
return 0;
}
|