#include using namespace std; using LL = long long int; #define incII(i, l, r) for(LL i = (l) ; i <= (r); i++) #define incID(i, l, r) for(LL i = (l) ; i < (r); i++) #define incCI(i, l, r) for(LL i = (l) + 1; i <= (r); i++) #define incCD(i, l, r) for(LL i = (l) + 1; i < (r); i++) #define decII(i, l, r) for(LL i = (r) ; i >= (l); i--) #define decID(i, l, r) for(LL i = (r) - 1; i >= (l); i--) #define decCI(i, l, r) for(LL i = (r) ; i > (l); i--) #define decCD(i, l, r) for(LL i = (r) - 1; i > (l); i--) #define inc(i, n) incID(i, 0, n) #define dec(i, n) decID(i, 0, n) #define inc1(i, n) incII(i, 1, n) #define dec1(i, n) decII(i, 1, n) auto inII = [](auto v, auto l, auto r) { return (l <= v && v <= r); }; auto inID = [](auto v, auto l, auto r) { return (l <= v && v < r); }; auto inCI = [](auto v, auto l, auto r) { return (l < v && v <= r); }; auto inCD = [](auto v, auto l, auto r) { return (l < v && v < r); }; #define PB push_back #define EB emplace_back #define MP make_pair #define MT make_tuple #define FI first #define SE second #define FR front() #define BA back() #define ALL(v) v.begin(), v.end() #define RALL(v) v.rbegin(), v.rend() auto setmin = [](auto & a, auto b) { return (b < a ? a = b, true : false); }; auto setmax = [](auto & a, auto b) { return (b > a ? a = b, true : false); }; auto setmineq = [](auto & a, auto b) { return (b <= a ? a = b, true : false); }; auto setmaxeq = [](auto & a, auto b) { return (b >= a ? a = b, true : false); }; #define SC static_cast #define SI(v) SC(v.size()) #define SL(v) SC(v.size()) #define RF(e, v) for(auto & e: v) #define until(e) while(! (e)) #define if_not(e) if(! (e)) #define ef else if #define UR assert(false) #define CT continue #define RV(v) reverse(ALL(v)) auto * IS = & cin; // input elements (as a tuple) template void in_([[maybe_unused]] U & t) { } template void in_(U & t) { (* IS) >> get(t); in_(t); } template auto in() { tuple t; in_, 0, T ...>(t); return t; } // input an array template auto ain() { array a; inc(i, N) { (* IS) >> a[i]; } return a; } // input a (multi-dimensional) vector template T vin() { T v; (* IS) >> v; return v; } template auto vin(N n, M ... m) { vector(m ...))> v(n); inc(i, n) { v[i] = vin(m ...); } return v; } // input multi-column (as a tuple of vector) template void colin_([[maybe_unused]] U & t) { } template void colin_(U & t) { A a; (* IS) >> a; get(t).push_back(a); colin_(t); } template auto colin(int n) { tuple ...> t; inc(i, n) { colin_ ...>, 0, T ...>(t); } return t; } auto * OS = & cout; // output elements void out_([[maybe_unused]] string s) { } template void out_([[maybe_unused]] string s, A && a) { (* OS) << a; } template void out_(string s, A && a, B && ... b) { (* OS) << a << s; out_(s, b ...); } auto outF = [](auto x, auto y, auto z, auto ... a) { (* OS) << x; out_(y, a ...); (* OS) << z << flush; }; auto out = [](auto ... a) { outF("", " " , "\n", a ...); }; auto outS = [](auto ... a) { outF("", " " , " " , a ...); }; auto outL = [](auto ... a) { outF("", "\n", "\n", a ...); }; auto outN = [](auto ... a) { outF("", "" , "" , a ...); }; array SEQ_FMT = { "", " ", "" }; auto & SEQ_BEG = SEQ_FMT[0]; auto & SEQ_MID = SEQ_FMT[1]; auto & SEQ_END = SEQ_FMT[2]; // output a (multi-dimensional) vector template ostream & operator<<(ostream & os, vector const & v) { os << SEQ_BEG; inc(i, SI(v)) { os << (i == 0 ? "" : SEQ_MID) << v[i]; } return (os << SEQ_END); } template void vout_(T && v) { (* OS) << v; } template void vout_(T && v, A a, B ... b) { inc(i, SI(v)) { (* OS) << (i == 0 ? "" : a); vout_(v[i], b ...); } } template void vout(T && v, A a, B ... b) { vout_(v, b ...); (* OS) << a << flush; } // ---- ---- template class ModInt { private: LL v; pair ext_gcd(LL a, LL b) { if(b == 0) { assert(a == 1); return { 1, 0 }; } auto p = ext_gcd(b, a % b); return { p.SE, p.FI - (a / b) * p.SE }; } public: ModInt(LL vv = 0) { v = vv; if(abs(v) >= M) { v %= M; } if(v < 0) { v += M; } } LL get_v() { return v; } ModInt inv() { return ext_gcd(M, v).SE; } ModInt exp(LL b) { ModInt p = 1, a = v; if(b < 0) { a = a.inv(); b = -b; } while(b) { if(b & 1) { p *= a; } a *= a; b >>= 1; } return p; } friend bool operator< (ModInt a, ModInt b) { return (a.v < b.v); } friend bool operator> (ModInt a, ModInt b) { return (a.v > b.v); } friend bool operator<=(ModInt a, ModInt b) { return (a.v <= b.v); } friend bool operator>=(ModInt a, ModInt b) { return (a.v >= b.v); } friend bool operator==(ModInt a, ModInt b) { return (a.v == b.v); } friend bool operator!=(ModInt a, ModInt b) { return (a.v != b.v); } friend ModInt operator+ (ModInt a ) { return ModInt(+a.v); } friend ModInt operator- (ModInt a ) { return ModInt(-a.v); } friend ModInt operator+ (ModInt a, ModInt b) { return ModInt(a.v + b.v); } friend ModInt operator- (ModInt a, ModInt b) { return ModInt(a.v - b.v); } friend ModInt operator* (ModInt a, ModInt b) { return ModInt(a.v * b.v); } friend ModInt operator/ (ModInt a, ModInt b) { return a * b.inv(); } friend ModInt operator^ (ModInt a, LL b) { return a.exp(b); } friend ModInt & operator+=(ModInt & a, ModInt b) { return (a = a + b); } friend ModInt & operator-=(ModInt & a, ModInt b) { return (a = a - b); } friend ModInt & operator*=(ModInt & a, ModInt b) { return (a = a * b); } friend ModInt & operator/=(ModInt & a, ModInt b) { return (a = a / b); } friend ModInt & operator^=(ModInt & a, LL b) { return (a = a ^ b); } friend istream & operator>>(istream & s, ModInt & b) { s >> b.v; b = ModInt(b.v); return s; } friend ostream & operator<<(ostream & s, ModInt b) { return (s << b.v); } }; // ---- using MI = ModInt<1'000'000'007>; #define bit(b, i) (((b) >> (i)) & 1) #define PC __builtin_popcountll #define BL(a) (a ? 64 - __builtin_clzll(a) : 0) int main() { auto [h, w, x] = in(); auto a = vin(h); auto b = vin(w); MI ans = 1; inc(k, x) { LL sa = 0, sb = 0; RF(e, a) { sa += bit(e, k); } RF(e, b) { sb += bit(e, k); } if(sa % 2 != sb % 2) { ans = 0; break; } ans *= MI(2) ^ ((h - 1) * (w - 1)); } out(ans); }