#include #include #include #include #include #include #include #include #include #include #include // https://github.com/yosupo06/library-checker-problems/blob/ac1ddf5011509c3d3960c33389291eed23a9ecc7/math/kth_root_mod/sol/correct.cpp namespace library_checker_problems { long long pow(long long a, long long n, long long p) { long long r=1; for (;n>0;n>>=1,a=a*a%p)if(n%2==1)r=r*a%p; return r; } int cnt(long long a,long long base,long long p) { int ret=0; while (a!=1) { a=pow(a,base,p); ++ret; } return ret; } long long inv(long long a, long long p) { a%=p; long long u=1, v=0; long long b=p; while (b>0) { long long q=a/b; a%=b; u-=v*q%p; u=(u%p+p)%p; { u^=v;v^=u;u^=v; a^=b;b^=a;a^=b; } } return u<0?u+p:u; } long long gcd(long long a,long long b) { return a==0?b:gcd(b%a,a); } long long peth_root(long long a,long long p,int e,long long mod) { long long q=mod-1; int s=0; while (q%p==0) { q/=p; ++s; } long long pe=pow(p,e,mod); long long ans=pow(a,((pe-1)*inv(q,pe)%pe*q+1)/pe,mod); long long c=2; while (pow(c,(mod-1)/p,mod)==1) ++c; c=pow(c,q,mod); std::map map; long long add=1; int v=(int)std::sqrt((double)(s-e)*p)+1; long long mul=pow(c,v*pow(p,s-1,mod-1)%(mod-1),mod); for (int i=0;i<=v;++i) { map[add]=i; add=add*mul%mod; } mul=inv(pow(c,pow(p,s-1,mod-1),mod),mod); for (int i=e;i0&&a%p==0)return 0; k%=p-1; long long g=gcd(k,p-1); if (pow(a,(p-1)/g,p)!=1) return -1; a=pow(a,inv(k/g,(p-1)/g),p); for (long long div=2;div*div<=g;++div) { int sz=0; while (g%div==0) { g/=div; ++sz; } if (sz>0) { long long b=peth_root(a,div,sz,p); a=b; } } if (g>1) a=peth_root(a,g,1,p); return a; } } // namespace library_checker_problems using mint = atcoder::static_modint<943718401>; // <嘘解法 (WA)> // 3 乗根を求めようとする。 mint S(const int n, mint x, std::vector a, std::vector b, std::vector c) { assert(n == std::ssize(a) - 1 && n == std::ssize(b) - 1 && n == std::ssize(c) - 1); if (x == 0) { mint s = 0; s += std::inner_product(a.begin(), a.end(), b.begin(), mint::raw(0)) * c[0]; s += std::inner_product(std::next(a.begin()), a.end(), std::next(c.begin()), mint::raw(0)) * b[0]; return s; } const int cubic_root = library_checker_problems::kth_root(x.val(), 3, mint::mod()); assert(cubic_root != -1); x = mint::raw(cubic_root); const auto T = [](const int i) -> std::int64_t { return std::int64_t{i} * i * (i); }; std::ranges::for_each( a, [&x, T, i = 0](mint& e) mutable -> void { e *= x.pow(T(i++)); }); const mint inv = x.inv(); std::ranges::for_each( b, [&inv, T, i = 0](mint& e) mutable -> void { e *= inv.pow(T(i++)); }); std::ranges::for_each( c, [&inv, T, i = 0](mint& e) mutable -> void { e *= inv.pow(T(i++)); }); const std::vector s = atcoder::convolution(b, c); return std::inner_product(a.begin(), a.end(), s.begin(), mint::raw(0)); } int main() { constexpr int kMaxN = 200000; const auto GetMint = []() -> mint { int x; std::cin >> x; assert(0 <= x && x < mint::mod()); return mint::raw(x); }; int n; std::cin >> n; assert(0 <= n && n <= kMaxN); const mint x = GetMint(); std::vector a(n + 1), b(n + 1), c(n + 1); std::ranges::for_each(a, [GetMint](mint& x) -> void { x = GetMint(); }); std::ranges::for_each(b, [GetMint](mint& x) -> void { x = GetMint(); }); std::ranges::for_each(c, [GetMint](mint& x) -> void { x = GetMint(); }); std::cout << S(n, x, a, b, c).val() << '\n'; return 0; }