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/*constexpr ll mod = 998244353; @\hl{NTT only}@
constexpr ll root = 3;*/
using cplx = complex<double>;
//void fft(vector<ll> &a, bool inverse = 0) { @\hl{NTT, xor, or, and}@
void fft(vector<cplx>& a, bool inverse = 0) {
int n = a.size();
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); @\hl{NTT only}@
if (inverse) ws = powMod(ws, mod - 2, mod);*/
double angle = PI / s * (inverse ? -1 : 1);
cplx ws(cos(angle), sin(angle));
for (int j = 0; j < n; j+= 2 * s) {
//ll w = 1; @\hl{NTT only}@
cplx w = 1;
for (int k = 0; k < s; k++) {
/*ll u = a[j + k], t = a[j + s + k] * w; @\hl{NTT only}@
t %= mod;
a[j + k] = (u + t) % mod;
a[j + s + k] = (u - t + mod) % mod;
w = (w * ws) % mod;*/
/*ll u = a[j + k], t = a[j + s + k]; @\hl{xor only}@
a[j + k] = u + t;
a[j + s + k] = u - t;*/
/*if (!inverse) { @\hl{or only}@
a[j + k] = u + t;
a[j + s + k] = u;
} else {
a[j + k] = t;
a[j + s + k] = u - t;
}*/
/*if (!inverse) { @\hl{and only}@
a[j + k] = t;
a[j + s + k] = u + t;
} else {
a[j + k] = t - u;
a[j + s + k] = u;
}*/
cplx u = a[j + k], t = a[j + s + k] * w;
a[j + k] = u + t;
a[j + s + k] = u - t;
if (inverse) a[j + k] /= 2, a[j + s + k] /= 2;
w *= ws;
}}}
/*if (inverse) { @\hl{NTT only}@
ll div = powMod(n, mod - 2, mod);
for (ll i = 0; i < n; i++) {
a[i] = (a[i] * div) % mod;
}}*/
/*if (inverse) { @\hl{xor only}@
for (ll i = 0; i < n; i++) {
a[i] /= n;
}}*/
}
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