Create grader.py

library/grader.py

@@ -0,0 +1,39 @@
+x = input()
+
+mat = [[0,0,1,0],[0,1,0,1],[1,0,2,0],[0,2,0,1]]
+mod = 10**9+7
+
+def egcd(a, b):
+    if a == 0:
+        return (b, 0, 1)
+    else:
+        g, y, x = egcd(b % a, a)
+        return (g, x - (b // a) * y, y)
+
+def modinv(a, m):
+    g, x, y = egcd(a, m)
+    if g != 1:
+        raise Exception('modular inverse does not exist')
+    else:
+        return x % m
+
+def matmult(mtx_a, mtx_b, mod):
+    tpos_b = zip( *mtx_b)
+    rtn = [[ sum( ea*eb for ea,eb in zip(a,b))%mod for b in tpos_b] for a in mtx_a]
+    return rtn
+
+def trace(A):
+    return sum(A[j][j] for j in range(len(A)))
+
+def matpow(A, p):
+    ret = A
+    for bit in bin(p)[3:]:
+        ret = matmult(ret, ret, mod)
+        if bit=='1':
+            ret = matmult(ret, A, mod)
+    return ret
+
+inv4 = modinv(4, mod)
+ans = trace(matpow(mat, x))%mod
+ans = (ans * inv4)% mod
+print ans