Why the function is failing in case of numbers greater than 48 digits?

I am trying to find

(a^b) % mod

where b and mod is upto 10^9, while l can be really large i have tested upto 48 digits with success
using this relation

(a^b) % mod = (a%mod)^b % mod

#define ll long long int
ll powerLL(ll x, ll n,ll MOD)
        {

        ll result = 1;
   

 while (n) {
        if (n & 1)
            result = result * x % MOD;
        n = n / 2;
        x = x * x % MOD;
    }
    return result;
}


ll powerStrings(string sa, string sb,ll MOD)
{


    ll a = 0, b = 0;


    for (size_t i = 0; i < sa.length(); i++)
        a = (a * 10 + (sa[i] - '0')) % MOD;

    for (size_t i = 0; i < sb.length(); i++)
        b = (b * 10 + (sb[i] - '0')) % (MOD - 1);

    return powerLL(a, b,MOD);
}

powerStrings("5109109785634228366587086207094636370893763284000","362323789",354252525) returns 208624800 but it should return 323419500. In this case a is 49 digits

powerStrings("300510498717329829809207642824818434714870652000","362323489",354255221) returns 282740484 , which is correct. In this case a is 48 digits

Is something wrong with the code or I will have to use other method of doing the same??