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Copy path13075.py
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13075.py
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import sys
sys.setrecursionlimit(10**6)
input=lambda:sys.stdin.readline().rstrip()
fimtx=[[1,1],[1,0]]
mod=10**9
def matrix_mul(N,a,b,mod):
c=[[0]*N for _ in range(N)]
for i in range(N):
for j in range(N):
c[i][j]=sum(a[i][k]*b[k][j] for k in range(N))%mod
return c
def matrix_pow(A,Matrix,b,mod):
if b==1:
for i in range(A):
for j in range(A):
Matrix[i][j]%=mod
return Matrix
elif b%2==0:
return matrix_pow(A,matrix_mul(A,Matrix,Matrix,mod),b//2,mod)
else:
return matrix_mul(A,Matrix,matrix_pow(A,matrix_mul(A,Matrix,Matrix,mod),b//2,mod),mod)
for _ in range(int(input())):
n=int(input())
if n==1:
print(1)
else:
ans=matrix_pow(2,fimtx,n-1,mod)
print(ans[0][0])