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vector<ll> mul(vector<ll> a, vector<ll> b) {
int n = 1 << bit_width(size(a) + size(b) - 1);
a.resize(n), b.resize(n);
ntt(a), ntt(b);
for (int i=0; i<n; i++) a[i] = a[i] * b[i] % mod;
ntt(a, true);
return a;
}
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