201,600 Degree Star-Preliminary (Astar round2a) AII X

Problem Description

F (X,m) represents an M-digit number that is all composed of a number x. Please calculate whether the following formula is true:

F (x,m) mod k≡c

Input

The first line is an integer t, which represents the T group data. One row for each set of test data, containing four digits x,m,k,c

1≤x≤9

1≤m≤10^10

0≤c<k≤10,000

Output

For each set of data, output two lines: The first line of output: "Case #i:". I represents the test data for group I. The second line output "Yes" or "No", representing four numbers, whether it can satisfy the formula given in the topic.

Sample Input

3

1 3 5 2

1 3 5 1

3 5 99 69
Sample Output

Case #1:

No

Case #2:

Yes

Case #3:

Yes

Hint

For the first set of test data: 111 MoD 5 = 1, the formula is not true, so the answer is "no", and the second set of test data satisfies the above formula, so the answer is "yes".

Xxxxxxx|xx*xx%k = = C
Because of k<=10000, the remainder range is within [0,10000], so define f[10000] (for labeling purposes)
Because I can not use the M-bit x directly to the K, consider periodicity, make t=0, continue to do Operation T= (t*10+x)%k,f[t]=r (array f is initialized to 0),
to the R (up to 10001) times (this is actually equal to the result of the R-bit x for the K-remainder), there must be duplicate values,
At this point, r-f[t] is the cycle T, that is, we take the T-bit x forward, the result of the K-remainder is still t, so we just need to do it again (M-f[t])%T
(t*10+x)%k operation, which greatly reduces run time

#include <stdio.h>#definell Long LongintOK (intX,ll m,intKintc) {    intf[10000] = {0},r,t=0, left;  for(r=1; r<=m;r++) {T= (Ten*T+X)%K; if(F[t]) { left= (int) ((M-f[t])% (rf[t]));  while(left--) {T= (Ten*T+X)%K; }            returnt = =C; } F[t]=R; }    returnt = = C;//m must be less than 10001}intMain () {intT,x,k,c,i=1;    ll m; scanf ("%d",&T);  while(t--) {scanf ("%d%lld%d%d",&x,&m,&k,&c); printf ("Case #%d\n", i++); Puts (OK (x,m,k,c)?"Yes":"No"); }    return 0;}//1 5 5 1 Yes//1 3 5 2 No//1 3 5 1 Yes//3 5 Yes//8 10000000000 No//7 9999998777 Yes

201,600 Degree Star-Preliminary (Astar round2a) AII X