d := 100;
m := 100;
d,m;
p := 1125899906842597;
n := 1;

Z := IntegerRing();
Zx<x> := PolynomialRing(Z);

getpoly := function(d,m,p)
    n := p^m;
    /*C := [ Random(-n,n) : i in [0..d-1] ];*/
    C := [ Random(1,n) : i in [0..d-1] ];
    g := Zx!C;
    return x^d+g;
end function;

f := getpoly(d,m,p);
g := getpoly(d,m,p);
time for i in [1..10*n] do a := f*g; end for;

height := function(f)
   C := Coefficients(f);
   h := 0;
   for c in C do 
       if Abs(c) gt h then h := Abs(c); end if;
   end for;
   return(h);
end function;

FactorBound := function(a)
    d := Degree(a);
    return 2^d*height(a)*Ceiling(Sqrt(d+1));
end function;

Zp<y> := PolynomialRing(Integers(p));
fp := Zp!f;
gp := Zp!g;
Gcd(fp,gp);
q := p;
h := 2*Max(height(f),height(g));  /* assumes you know the height of the answer!! */
h := 2*FactorBound(a);
k := 1;
while q lt h do q := q^2; k := k+1; end while;
k;
Zpk<z> := PolynomialRing(Integers(q));
time for i in [1..n] do H := HenselLift(a,[fp,gp],Zpk); end for;
zero := H[1]*H[2]-a;
zero;