/*  slfpfprd.cpp  by K.Tsuru  */
// function ID 2012   DRADIX    since ver 2.182
// first version made on 24 Apr 2010
/***********************************************************
make product
p[0]^a*p[1]^b*p[2]^c...
***********************************************************/
#ifndef SN_H
#include "sn.h"
#endif
SLong PrimeFactorProduct(const SNBlock <primeFactor>& pf, int n) {
    SNBlock <SLong> w(4);
    int wc = 0, pc = 0;
    int pow = pf(0).power;
    SNBlock <SLong> wSL(n);

    while(pc < n) {
        // bind factors with the same power
        // ...(a^p)(b^p)(c^p)... --> ...(abc)^p...
        int k = 0;
        for(; pow == pf(pc).power; pc++) {  // while the same power
            w.reserve(k);
            w[k].SetInt( pf(pc).prime );
            k++;
        }
        if(k > 1) { // k : number of the same power
            wSL[wc] = BothSideProduct(w, k, false); // sort is not necessary
        } else wSL[wc] = w[0];  // only one element
        if(pow > 1) wSL[wc] = Lpow( wSL[wc], (ulong)pow );  // wSL[wc]^pow
        wc++;
        pow = pf(pc).power; // next power
    }
    SLong Q = TournamentProduct(wSL, wc);
    return Q;
}