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constexpr ll mod = 998244353;
constexpr ll root = 3;
void fft(vector<ll>& a, bool inverse = 0) {
int n = sz(a);
for (int i = 0, j = 1; j < n - 1; ++j) {
for (int k = n >> 1; k > (i ^= k); k >>= 1);
if (j < i) swap(a[i], a[j]);
}
for (int s = 1; s < n; s *= 2) {
ll ws = powMod(root, (mod - 1) / s >> 1, mod);
if (inverse) ws = powMod(ws, mod - 2, mod);
for (int j = 0; j < n; j+= 2 * s) {
ll w = 1;
for (int k = 0; k < s; k++) {
ll u = a[j + k], t = a[j + s + k] * w;
t %= mod;
a[j + k] = (u + t) % mod;
a[j + s + k] = (u - t + mod) % mod;
w *= ws;
w %= mod;
}}}
if (inverse) {
ll div = powMod(n, mod - 2, mod);
for (ll i = 0; i < n; i++) {
a[i] *= div;
a[i] %= mod;
}}}
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