C Programming Language

Hi! I've recently started learning C and I've been getting stuck on the basic tasks cuz I keep overcomplicating them T-T Could anyone please help me with this specific task?

Problem Statement

You have a digit sequence S of length 4. You are wondering which of the following formats S is in:

• YYMM format: the last two digits of the year and the two-digit representation of the month (example: 01 for January), concatenated in this order
• MMYY format: the two-digit representation of the month and the last two digits of the year, concatenated in this order

If S is valid in only YYMM format, print YYMM; if S is valid in only MMYY format, print MMYY; if S is valid in both formats, print AMBIGUOUS; if S is valid in neither format, print NA.

Constraints
－ S is a digit sequence of length 4.

Sample Input 1
1905

Sample Output 1
YYMM
May XX19 is a valid date, but 19 is not valid as a month. Thus, this string is only valid in YYMM format.

Sample Input 2
0112

Sample 2
AMBIGUOUS
Both December XX01 and January XX12 are valid dates. Thus, this string is valid in both formats.

Sample Input 3
1700

Sample Output 3
NA
Neither 0 nor 17 is valid as a month. Thus, this string is valid in neither format.

The code I wrote for this is:

#include <stdio.h>

int main(){
    int S;
    scanf("%d", &S);
    int p1 = S/100;
    int p2 = S%100;
    if (p1!=0 && p1<=12){
        if(p2!=0 && p2<=12){
            printf("AMBIGUOUS");
        }
        else if (p2>=13){
            printf("MMYY");
        }
        else{
            printf("NA");
        }
    }
    else if (p1>=13){
        
        if(p2!=0 && p2<=12){
            printf("YYMM");
        }
        else {
            printf("NA");
        }
    }
   return 0;
}

It passed the 7 checks in the system, but failed on the 8th and I have no idea what kind of values are on the 8th check... Thanks to anyone for reading this far!