k = 23
#mod = 10**9
T = np.zeros(((k+1)*k,(k+1)*k)).astype(np.int64)
init = np.zeros((k+1)*k).astype(np.int64)
init[0] = 1
for d in xrange(10):
for i in xrange((k+1)*k):
s = i/k #sum
m = i%k #mod-state
m_new = ((10*m) + d) % k
if s + d <= k:
T[k*(s+d) + m_new,i] = 1
r1 = pe.matrix_mod_exp(n,T,init,2**9)[k*k]
r2 = pe.matrix_mod_exp(n,T,init,5**9)[k*k]
print "mod 2^9: " + str(r1) + " mod 5^9 " + str(r2)
def G(n): global T,init v = matrix_mod_exp(n-1,T,init,mod) return v[-1]
def FibboEval(n,x,mod): I = np.array([1,x,0],dtype=np.int64) A = np.array([[1,0,0],[x,x,x*x],[0,1,0]],dtype=np.int64) res = matrix_mod_exp(n-1,A,I,mod) return res[1]
from proj_euler import matrix_mod_exp,MillerRabin
import numpy as np
from CR_NEWTON_LAGRANGE import Lagrange_cr
I = np.array([1,0],dtype=np.int64)
T = np.array([[1,1],[1,0]],dtype=np.int64)
start = 10**14
mod = 1234567891011
m1=1957137
m2=630803
if not m2*m1==mod:
raise Exception("Incorrect modulus factorization.")
res1=matrix_mod_exp(start,T,I,m1)
res2=matrix_mod_exp(start,T,I,m2)
prev = Lagrange_cr((int(res1[1]),int(res2[1])),(m1,m2))
curr = Lagrange_cr((int(res1[0]),int(res2[0])),(m1,m2))
n = 10**5
count = 0
i = start+1
s = 0
while count < n:
if MillerRabin(i):
s += curr
if s > mod:
s -= mod
count += 1
curr,prev = curr+prev,curr
