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| #include <cstdio>
#include <vector>
#include <algorithm>
using namespace std;
typedef long long LL;
const int N = 1e6 + 10, mod = 998244353;
int 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 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] = (p + q) % mod, x[i | j | mid] = (p - q) % mod;
}
}
if (~op) return;
int itot = binpow(tot);
for (int i = 0; i < tot; ++i)
x[i] = (LL)x[i] * itot % mod;
}
class LargeNumber
{
int sign;
vector <LL> w;
friend void adj(LargeNumber &x)
{
while (!x.w.empty() && !x.w.back()) x.w.pop_back();
if (x.w.empty()) x.sign = 0;
}
friend int cmp(LargeNumber &x, LargeNumber &y)
{
if (x.sign ^ y.sign)
return x.sign < y.sign ? -1 : 1;
if (x.size() ^ y.size())
return x.size() < y.size() ? -1 : 1;
for (int i = x.size() - 1; ~i; i--)
if (x[i] ^ y[i]) return x[i] < y[i] ? -1 : 1;
return 0;
}
friend LargeNumber add(LargeNumber &x, LargeNumber &y)
{
LargeNumber res;
res.sign = 1;
res.w.resize(max(x.size(), y.size()) + 1);
for (int i = 0; i + 1 < res.size(); i++)
{
if (i < x.size()) res[i] += x[i];
if (i < y.size()) res[i] += y[i];
if (res[i] > 9) res[i + 1]++, res[i] -= 10;
}
adj(res);
return res;
}
friend LargeNumber dec(LargeNumber &x, LargeNumber &y)
{
LargeNumber res;
res.sign = 1;
res.w.resize(max(x.size(), y.size()));
for (int i = 0; i < res.size(); i++)
{
if (i < x.size()) res[i] += x[i];
if (i < y.size()) res[i] -= y[i];
if (res[i] < 0) res[i + 1]--, res[i] += 10;
}
adj(res);
return res;
}
friend void div2(LargeNumber &x)
{
bool flag = false;
for (int i = x.size() - 1; ~i; i--)
{
int t = x[i] + flag * 10;
flag = t & 1;
x[i] = t >> 1;
}
adj(x);
}
public:
LargeNumber() {}
template <class Type>
LargeNumber(Type x)
{
if (x < 0) sign = -1, x = ~x + 1;
else if (x > 0) sign = 1;
else sign = 0;
while (x)
w.push_back(x % 10), x /= 10;
}
void input()
{
sign = 1;
char c;
while ((c = getchar()) < '0' || c > '9')
c == '-' && (sign = -1);
w.push_back(c - '0');
while ((c = getchar()) >= '0' && c <= '9')
w.push_back(c - '0');
reverse(w.begin(), w.end());
}
void output()
{
if (!sign) putchar('0');
if (sign == -1) putchar('-');
for (int i = w.size() - 1; ~i; i--)
putchar(w[i] + '0');
}
int size () { return w.size(); }
LL &operator[](LL x) { return w[x]; }
friend bool operator!(LargeNumber x) { return !x.sign; }
friend LargeNumber operator-(LargeNumber x) { x.sign *= -1; return x; }
friend bool operator!=(LargeNumber x, LargeNumber y) { return cmp(x, y); }
friend bool operator==(LargeNumber x, LargeNumber y) { return !cmp(x, y); }
friend bool operator<(LargeNumber x, LargeNumber y) { return cmp(x, y) == -1; }
friend bool operator>(LargeNumber x, LargeNumber y) { return cmp(x, y) == 1; }
friend bool operator<=(LargeNumber x, LargeNumber y) { return cmp(x, y) ^ 1; }
friend bool operator>=(LargeNumber x, LargeNumber y) { return ~cmp(x, y); }
friend LargeNumber operator*(LargeNumber x, LargeNumber y)
{
LargeNumber res;
res.sign = x.sign * y.sign;
res.w.resize(x.size() + y.size());
static int A[N], B[N], C[N];
int bit = 0;
while (1 << bit < res.size()) ++bit;
int tot = 1 << bit;
for (int i = 0; i < x.size(); ++i) A[i] = x.w[i];
for (int i = 0; i < y.size(); ++i) B[i] = y.w[i];
for (int i = x.size(); i < tot; i++) A[i] = 0;
for (int i = y.size(); i < tot; i++) B[i] = 0;
ntt(A, bit, 1), ntt(B, bit, 1);
for (int i = 0; i < tot; i++)
C[i] = (LL)A[i] * B[i] % mod;
ntt(C, bit, -1);
for (int i = 0; i < res.size(); i++)
res[i] = (C[i] + mod) % mod;
for (int i = 0; i + 1 < res.size(); i++)
{
res[i + 1] += res[i] / 10;
res[i] %= 10;
}
adj(res);
return res;
}
friend LargeNumber operator/(LargeNumber x, int k)
{
LargeNumber res = x;
if (k < 0) k = -k, res.sign ^= 1;
for (int i = res.size() - 1; ~i; --i)
{
if (i) res[i - 1] += res[i] % k * 10;
res[i] /= k;
}
adj(res);
return res;
}
friend LargeNumber operator%(LargeNumber x, int k) { return x - x / k * k; }
friend LargeNumber operator+(LargeNumber x, LargeNumber y)
{
if (!x.sign) return y;
if (!y.sign) return x;
if (x.sign == 1 && y.sign == 1) return add(x, y);
if (x.sign == -1 && y.sign == -1)
{
LargeNumber res = add(x, y);
res.sign = -1;
return res;
}
if (x.sign == -1 && y.sign == 1) swap(x, y);
y.sign = 1;
if (x < y)
{
LargeNumber res = dec(y, x);
res.sign = -1;
return res;
}
return dec(x, y);
}
friend LargeNumber operator-(LargeNumber x, LargeNumber y) { return x + (-y); }
friend LargeNumber operator^(LargeNumber b, LargeNumber k)
{
LargeNumber res(1);
for (; k.sign == 1; b = b * b, div2(k))
if (k[0] & 1) res = res * b;
return res;
}
friend LargeNumber operator++(LargeNumber &x) { return x = (x + LargeNumber(1)); }
friend LargeNumber operator--(LargeNumber &x) { return x = (x - LargeNumber(1)); }
friend LargeNumber operator+=(LargeNumber &x, const LargeNumber y) { return x = (x + y); }
friend LargeNumber operator-=(LargeNumber &x, const LargeNumber y) { return x = (x - y); }
friend LargeNumber operator*=(LargeNumber &x, const LargeNumber y) { return x = (x * y); }
friend LargeNumber operator/=(LargeNumber &x, const int y) { return x = (x / y); }
friend LargeNumber operator%=(LargeNumber &x, const int y) { return x = (x % y); }
friend LargeNumber operator^=(LargeNumber &x, const LargeNumber y) { return x = (x ^ y); }
friend void swap(LargeNumber &x, LargeNumber &y) { LargeNumber tmp = x; x = y, y = tmp; }
friend LargeNumber abs(LargeNumber x) { if (x.sign < 0) x.sign = 1; return x; }
friend void chkmin(LargeNumber &x, LargeNumber k) { if (k < x) x = k; }
friend void chkmax(LargeNumber &x, LargeNumber k) { if (k > x) x = k; }
friend LargeNumber min(const LargeNumber &x, const LargeNumber &y) { return x > y ? y : x; }
friend LargeNumber max(const LargeNumber &x, const LargeNumber &y) { return x > y ? x : y; }
};
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