Subsequences forming Strings

#include<bits/stdc++.h>
using namespace std;
#define D(x) cout<<#x<<" = "<<x<<endl;
#define mx 100
#define mod 1000000007
//int dx[]={1,0,-1,0};int dy[]={0,1,0,-1}; //4 Direction
//int dx[]={1,1,0,-1,-1,-1,0,1};int dy[]={0,1,1,1,0,-1,-1,-1};//8 direction
//int dx[]={2,1,-1,-2,-2,-1,1,2};int dy[]={1,2,2,1,-1,-2,-2,-1};//Knight Direction
//int dx[]={2,1,-1,-2,-1,1};int dy[]={0,1,1,0,-1,-1}; //Hexagonal Direction

int ab = 0;
int ba = 1;

string A,B,C;
int total = 0;
int cs = 1;
int dp[mx+5][mx+5][mx+5][2];
int vis[mx+5][mx+5][mx+5][2];


int solve(int a, int b, int c, int ck)
{
    int ret = 0;
    if(c == 0) return 1;
    if(a == 0 && b == 0) return 0;
    if(vis[a][b][c][ck] == cs)
        return dp[a][b][c][ck];
    vis[a][b][c][ck] = cs;

    if(a>0 && ck == ab)
    {
        ret = (ret + solve(a-1, b, c, ab))%mod;
        if(A[a-1] == C[c-1]){
            ret = (ret+ solve(a-1, b, c-1, ab))%mod;
            if(c-1>0) ret = (ret + solve(a-1,b,c-1,ba))%mod;
        }
    }
    if(b>0 && ck == ba)
    {
        ret  = (ret + solve(a, b-1, c, ba))%mod;
        if(B[b-1] == C[c-1])
        {
            ret = (ret + solve(a, b-1,c-1, ba))%mod;
            if(c-1>0) ret = (ret + solve(a, b-1, c-1, ab))%mod;
        }
    }
    return dp[a][b][c][ck] =ret;
}



int main()
{
    int tc;
    cin>>tc;
    while(tc--)
    {
       // memset(dp,-1,sizeof dp);
        total = 0;
        cin>>A>>B>>C;
        int la, lb, lc;
        la = A.length();
        lb = B.length();
        lc = C.length();
        int ans = (solve(la, lb, lc,ab) + solve(la, lb, lc,ba)) %mod;
        printf("Case %d: %d\n",cs++,ans);
        // D(ans);
        //D(total);
    }
    return 0;


}