Use sieve method instead of algebraic method

13/part2

@@ -1,50 +1,32 @@
 #!/usr/bin/python3
+import time
 
-def ext_euclid(a, b):
-    """
-    returns solutions x and y for equation ax + by = gcd(a, b)
-    """
-
-    (old_r, r) = (a, b)
-    (old_s, s) = (1, 0)
-    (old_t, t) = (0, 1)
-
-    while r:
-        quotient = old_r // r
-        (old_r, r) = (r, old_r - quotient * r)
-        (old_s, s) = (s, old_s - quotient * s)
-        (old_t, t) = (t, old_t - quotient * t)
-    return old_s, old_t, old_r
-
-n = []
-a = []
+def shuttle_generator():
     with open("input") as fh:
         now = int(fh.readline())
         for i, x in enumerate(fh.readline().split(",")):
             if x != "x":
                 x = int(x)
-            n.append(x)
-            a.append((x - i) % x)
+                yield i, x
 
-print(n)
-print(a)
+shuttle = shuttle_generator()
 
-n1 = n.pop()
-n2 = n.pop()
-a1 = a.pop()
-a2 = a.pop()
-m1, m2, _ = ext_euclid(n1, n2)
-assert _ == 1
-x = a1 * m2 * n2 + a2 * m1 * n1
-print(x)
-while n:
-    n1 = n1 * n2
-    a1 = x
+def check(t, tests):
+    for i, n in tests:
+        if (t + i) % n != 0:
+            return False
+    return True
 
-    n2 = n.pop()
-    a2 = a.pop()
+t = 0
+step = 1
+n = 1
+tests = []
+while True:
+    if check(t, tests):
+        print(t, "matches", tests)
+        time.sleep(2)
+        step *= n
+        i, n = next(shuttle)
+        tests.append((i, n))
+    t += step
 
-    m1, m2, _ = ext_euclid(n1, n2)
-    assert _ == 1
-    x = a1 * m2 * n2 + a2 * m1 * n1
-    print(x)