class Modulo_Error(Exception): pass class Modulo(): def __init__(self,a,n): self.a=a%n self.n=n def __str__(self): return "{} (mod {})".format(self.a,self.n) def __repr__(self): return self.__str__() #+,- def __pos__(self): return self def __neg__(self): return Modulo(-self.a,self.n) #等号,不等号 def __eq__(self,other): if isinstance(other,Modulo): return (self.a==other.a) and (self.n==other.n) elif isinstance(other,int): return (self-other).a==0 def __neq__(self,other): return not(self==other) def __le__(self,other): a,p=self.a,self.n b,q=other.a,other.n return (a-b)%q==0 and p%q==0 def __ge__(self,other): return other<=self def __lt__(self,other): return (self<=other) and (self!=other) def __gt__(self,other): return (self>=other) and (self!=other) #加法 def __add__(self,other): if isinstance(other,Modulo): if self.n!=other.n: raise Modulo_Error("異なる法同士の演算です.") return Modulo(self.a+other.a,self.n) elif isinstance(other,int): return Modulo(self.a+other,self.n) def __radd__(self,other): if isinstance(other,int): return Modulo(self.a+other,self.n) #減法 def __sub__(self,other): return self+(-other) def __rsub__(self,other): if isinstance(other,int): return -self+other #乗法 def __mul__(self,other): if isinstance(other,Modulo): if self.n!=other.n: raise Modulo_Error("異なる法同士の演算です.") return Modulo(self.a*other.a,self.n) elif isinstance(other,int): return Modulo(self.a*other,self.n) def __rmul__(self,other): if isinstance(other,int): return Modulo(self.a*other,self.n) #Modulo逆数 def inverse(self): return self.Modulo_Inverse() def Modulo_Inverse(self): x0, y0, x1, y1 = 1, 0, 0, 1 a,b=self.a,self.n while b != 0: q, a, b = a // b, b, a % b x0, x1 = x1, x0 - q * x1 y0, y1 = y1, y0 - q * y1 if a!=1: raise Modulo_Error("{}の逆数が存在しません".format(self)) else: return Modulo(x0,self.n) #除法 def __truediv__(self,other): return self*(other.Modulo_Inverse()) def __rtruediv__(self,other): return other*(self.Modulo_Inverse()) #累乗 def __pow__(self,other): if isinstance(other,int): u=abs(other) r=Modulo(pow(self.a,u,self.n),self.n) if other>=0: return r else: return r.Modulo_Inverse() else: b,n=other.a,other.n if pow(self.a,n,self.n)!=1: raise Modulo_Error("矛盾なく定義できません.") else: return self**b def Factor_Modulo(N,M,Mode=0): """ Mode=0のとき:N! (mod M) を求める. Mode=1のとき:k! (mod M) (k=0,1,...,N) のリストも出力する. [計算量] O(N) """ if Mode==0: X=Modulo(1,M) for k in range(1,N+1): X*=k return X else: L=[Modulo(1,M)]*(N+1) for k in range(1,N+1): L[k]=k*L[k-1] return L def Factor_Modulo_with_Inverse(N,M): """ k=0,1,...,N に対する k! (mod M) と (k!)^(-1) (mod M) のリストを出力する. [入力] N,M:整数 M>0 [出力] 長さ N+1 のリストのタプル (F,G):F[k]=k! (mod M), G[k]=(k!)^(-1) (mod M) [計算量] O(N) """ assert M>0 F=Factor_Modulo(N,M,Mode=1) G=[0]*(N+1) G[-1]=F[-1].inverse() for k in range(N,0,-1): G[k-1]=k*G[k] return F,G #================================================ def nCr(n,r): return F[n]*G[r]*G[n-r] def nHr(n,r): return nCr(n+r-1,r) #================================================ N,K=map(int,input().split()) A=["*"]+list(map(int,input().split())) Mod=10**9+7 F,G=Factor_Modulo_with_Inverse(N+5,Mod) X=Modulo(0,Mod) L=[0]*(N+1); L[1]=Modulo(1,Mod) for i in range(2,N+1): L[i]=Modulo(i+K-1,Mod)/Modulo(i-1,Mod)*L[i-1] R=[0]*(N+1); R[N]=Modulo(1,Mod) for i in range(N-1,0,-1): R[i]=Modulo(N-i+K,Mod)/Modulo(N-i,Mod)*R[i+1] for i in range(1,N+1): X+=A[i]*L[i]*R[i] print(X.a)