#line 1 "2793.cpp" // #pragma GCC target("avx2,avx512f,avx512vl,avx512bw,avx512dq,avx512cd,avx512vbmi,avx512vbmi2,avx512vpopcntdq,avx512bitalg,bmi,bmi2,lzcnt,popcnt") // #pragma GCC optimize("Ofast") #line 2 "/home/sigma/comp/library/template.hpp" #include using namespace std; using ll = long long; using uint = unsigned int; using ull = unsigned long long; #define rep(i,n) for(int i=0;i=0;i--) #define per1(i,n) for(int i=int(n);i>0;i--) #define all(c) c.begin(),c.end() #define si(x) int(x.size()) #define pb push_back #define eb emplace_back #define fs first #define sc second template using V = vector; template using VV = vector>; template bool chmax(T& x, U y){ if(x bool chmin(T& x, U y){ if(y void mkuni(V& v){sort(all(v));v.erase(unique(all(v)),v.end());} template int lwb(const V& v, const T& a){return lower_bound(all(v),a) - v.begin();} template V Vec(size_t a) { return V(a); } template auto Vec(size_t a, Ts... ts) { return V(ts...))>(a, Vec(ts...)); } template ostream& operator<<(ostream& o,const pair &p){ return o<<"("< ostream& operator<<(ostream& o,const vector &vc){ o<<"{"; for(const T& v:vc) o< D divFloor(D a, D b){ return a / b - (((a ^ b) < 0 && a % b != 0) ? 1 : 0); } template D divCeil(D a, D b) { return a / b + (((a ^ b) > 0 && a % b != 0) ? 1 : 0); } /* x 0 1 2 3 4 5 6 7 8 9 bsr(x) -1 0 1 1 2 2 2 2 3 3 最上位bit */ int bsr(int x){ return x == 0 ? -1 : 31 ^ __builtin_clz(x); } int bsr(uint x){ return x == 0 ? -1 : 31 ^ __builtin_clz(x); } int bsr(ll x){ return x == 0 ? -1 : 63 ^ __builtin_clzll(x); } int bsr(ull x){ return x == 0 ? -1 : 63 ^ __builtin_clzll(x); } /* x 0 1 2 3 4 5 6 7 8 9 bsl(x) -1 0 1 0 2 0 1 0 3 0 最下位bit */ int bsl(int x){ if(x==0) return -1; return __builtin_ctz(x); } int bsl(uint x){ if(x==0) return -1; return __builtin_ctz(x); } int bsl(ll x){ if(x==0) return -1; return __builtin_ctzll(x); } int bsl(ull x){ if(x==0) return -1; return __builtin_ctzll(x); } template T rnd(T l,T r){ //[l,r) using D = uniform_int_distribution; static random_device rd; static mt19937 gen(rd()); return D(l,r-1)(gen); } template T rnd(T n){ //[0,n) return rnd(T(0),n); } #line 1 "/home/sigma/comp/library/math/mint.cpp" /* 任意mod なら template なくして costexpr の行消して global に unsigned int mod = 1; で cin>>mod してから使う 任意 mod はかなり遅いので、できれば "atcoder/modint" を使う */ template struct ModInt{ using uint = unsigned int; using ll = long long; using ull = unsigned long long; constexpr static uint mod = mod_; uint v; ModInt():v(0){} ModInt(ll _v):v(normS(_v%mod+mod)){} explicit operator bool() const {return v!=0;} static uint normS(const uint &x){return (x [0 , mod-1] static ModInt make(const uint &x){ModInt m; m.v=x; return m;} ModInt operator+(const ModInt& b) const { return make(normS(v+b.v));} ModInt operator-(const ModInt& b) const { return make(normS(v+mod-b.v));} ModInt operator-() const { return make(normS(mod-v)); } ModInt operator*(const ModInt& b) const { return make((ull)v*b.v%mod);} ModInt operator/(const ModInt& b) const { return *this*b.inv();} ModInt& operator+=(const ModInt& b){ return *this=*this+b;} ModInt& operator-=(const ModInt& b){ return *this=*this-b;} ModInt& operator*=(const ModInt& b){ return *this=*this*b;} ModInt& operator/=(const ModInt& b){ return *this=*this/b;} ModInt& operator++(int){ return *this=*this+1;} ModInt& operator--(int){ return *this=*this-1;} template friend ModInt operator+(T a, const ModInt& b){ return (ModInt(a) += b);} template friend ModInt operator-(T a, const ModInt& b){ return (ModInt(a) -= b);} template friend ModInt operator*(T a, const ModInt& b){ return (ModInt(a) *= b);} template friend ModInt operator/(T a, const ModInt& b){ return (ModInt(a) /= b);} ModInt pow(ll p) const { if(p<0) return inv().pow(-p); ModInt a = 1; ModInt x = *this; while(p){ if(p&1) a *= x; x *= x; p >>= 1; } return a; } ModInt inv() const { // should be prime return pow(mod-2); } // ll extgcd(ll a,ll b,ll &x,ll &y) const{ // ll p[]={a,1,0},q[]={b,0,1}; // while(*q){ // ll t=*p/ *q; // rep(i,3) swap(p[i]-=t*q[i],q[i]); // } // if(p[0]<0) rep(i,3) p[i]=-p[i]; // x=p[1],y=p[2]; // return p[0]; // } // ModInt inv() const { // ll x,y; // extgcd(v,mod,x,y); // return make(normS(x+mod)); // } bool operator==(const ModInt& b) const { return v==b.v;} bool operator!=(const ModInt& b) const { return v!=b.v;} bool operator<(const ModInt& b) const { return v>(istream &o,ModInt& x){ ll tmp; o>>tmp; x=ModInt(tmp); return o; } friend ostream& operator<<(ostream &o,const ModInt& x){ return o<; //using mint = ModInt<1000000007>; V fact,ifact,invs; // a,b >= 0 のみ mint Choose(int a,int b){ if(b<0 || a= 0 の範囲で、 Choose(a,b) = a(a-1)..(a-b+1) / b! mint Choose(int a,int b){ if(b<0 || a=0;i--) ifact[i] = ifact[i+1] * (i+1); rep1(i,N-1) invs[i] = fact[i-1] * ifact[i]; } #line 6 "2793.cpp" map,mint> memo; int K; mint dfs(V A){ int N = si(A)-1; if(N == 0) return 1; if(memo.count(A)) return memo[A]; mint res = 0; auto dfs2 = [&](auto&& self, int i, mint cur) -> void { if(i == N){ if(A[N] == 0){ A.pop_back(); res += dfs(A) * cur; A.eb(0); } return; } rep(v,A[N]+1){ A[i] += v; A[N] -= v; mint f = 1; if(v) f = mint(K).pow(v) - mint(K).pow(v-1); self(self,i+1,cur*f); A[i] -= v; A[N] += v; } }; dfs2(dfs2,0,1); return memo[A] = res; } mint brute(V A){ memo.clear(); A.insert(A.begin(),0); return dfs(A); } void TEST(){ cin >> K; while(true){ int N; cin >> N; V A(N); rep(i,N) cin >> A[i]; show(brute(A)); } } int main(){ cin.tie(0); ios::sync_with_stdio(false); //DON'T USE scanf/printf/puts !! cout << fixed << setprecision(20); // TEST(); int T; cin >> T; while(T--){ int N; mint K; cin >> N >> K; ll pw = 0; rep1(i,N){ ll a; cin >> a; pw += (a-1) * i; pw %= mint::mod-1; } mint ans = K.pow(pw) * (K-1).pow(N); mint s = 0; mint pK = 1; rep(i,N){ s += pK; ans *= s; pK *= K; } cout << ans << endl; } }