import sys sys.setrecursionlimit(10 ** 6) int1 = lambda x: int(x) - 1 p2D = lambda x: print(*x, sep="\n") def II(): return int(sys.stdin.readline()) def MI(): return map(int, sys.stdin.readline().split()) def LI(): return list(map(int, sys.stdin.readline().split())) def LLI(rows_number): return [LI() for _ in range(rows_number)] def SI(): return sys.stdin.readline()[:-1] class mint: def __init__(self, x): self.__x = x % md def __str__(self): return str(self.__x) def __add__(self, other): if isinstance(other, mint): other = other.__x return mint(self.__x + other) def __sub__(self, other): if isinstance(other, mint): other = other.__x return mint(self.__x - other) def __rsub__(self, other): return mint(other - self.__x) def __mul__(self, other): if isinstance(other, mint): other = other.__x return mint(self.__x * other) __radd__ = __add__ __rmul__ = __mul__ def __truediv__(self, other): if isinstance(other, mint): other = other.__x return mint(self.__x * pow(other, md - 2, md)) def __pow__(self, power, modulo=None): return mint(pow(self.__x, power, md)) class Fibonacci: def __init__(self, aa): n = len(aa) coff = [1] * n self.f0 = aa # 上2つは問題ごとに手作業で設定 # af(n)+bf(n+1)+cf(n+2)+df(n+3)=f(n+4)みたいなとき # coff=[a,b,c,d] # 初期値f0(f(0)からf(3)) ff = [[0] * n for _ in range(2 * n - 1)] for i in range(n): ff[i][i] = mint(1) for i in range(n, 2 * n - 1): ffi = ff[i] for j, c in enumerate(coff, i - n): ffj = ff[j] for k in range(n): ffi[k] += c * ffj[k] self.bn = 1 << (n - 1).bit_length() self.base = ff[self.bn] self.ff = ff self.n = n def __mm(self, aa, bb): n = self.n res = [0] * (n * 2 - 1) for i, a in enumerate(aa): for j, b in enumerate(bb): res[i + j] += a * b for i in range(n, 2 * n - 1): c = res[i] ffi = self.ff[i] for j in range(n): res[j] += c * ffi[j] return res[:n] def v(self, x): base = self.base aa = self.ff[x % self.bn] x //= self.bn while x: if x & 1: aa = self.__mm(aa, base) base = self.__mm(base, base) x >>= 1 return sum(a * f for a, f in zip(aa, self.f0)) class Sibonacci: def __init__(self, aa): n = len(aa)+1 coff = [-1]+[0]*(n-2)+[2] fb=Fibonacci(aa) f0=[fb.v(0)] for x in range(1,n): f0.append(f0[-1]+fb.v(x)) self.f0 = f0 # 上2つは問題ごとに手作業で設定 # af(n)+bf(n+1)+cf(n+2)+df(n+3)=f(n+4)みたいなとき # coff=[a,b,c,d] # 初期値f0(f(0)からf(3)) ff = [[0] * n for _ in range(2 * n - 1)] for i in range(n):ff[i][i] = mint(1) for i in range(n, 2 * n - 1): ffi = ff[i] for j, c in enumerate(coff, i - n): ffj = ff[j] for k in range(n): ffi[k] += c * ffj[k] self.bn = 1 << (n - 1).bit_length() self.base = ff[self.bn] self.ff = ff self.n = n def __mm(self, aa, bb): n = self.n res = [0] * (n * 2 - 1) for i, a in enumerate(aa): for j, b in enumerate(bb): res[i + j] += a * b for i in range(n, 2 * n - 1): c = res[i] ffi = self.ff[i] for j in range(n): res[j] += c * ffi[j] return res[:n] def v(self, x): base = self.base aa = self.ff[x % self.bn] x //= self.bn while x: if x & 1: aa = self.__mm(aa, base) base = self.__mm(base, base) x >>= 1 return sum(a * f for a, f in zip(aa, self.f0)) md=10**9+7 def main(): n,k=MI() f0=LI() s=Sibonacci(f0) print(s.v(k-1)-s.v(k-2),s.v(k-1)) main()