jasper

findpath[aset_, Mset_] :=
 Module[{mM, amax = Max[aset], f, path, adouble, adouble2, aremo,
   anext, mnext, mprime, tpath, k, parsum, ai, t},
  If[Length[Mset] == 0, Print["case 0"]; path = aset;,
   mM = Min[Mset];
   f = Length[Select[Mset, # < amax &]];
   If[f > 0,
    If[MemberQ[Mset, amax],
     Print["case 1"];
     adouble = Select[aset, Not[MemberQ[Mset, #]] &];
     adouble2 = Select[adouble, Not[MemberQ[Mset, # + amax]] &];
     (*guaranteed to exist by counting*)

     aremo = {adouble2[[1]], amax};
     anext = Select[aset, Not[MemberQ[aremo, #]] &];
     mnext =
      Select[Mset, # > amax + adouble2[[1]] &] - amax -
       adouble2[[1]];
     Print[anext, mnext];
     path = Flatten[{aremo, findpath[anext, mnext]}];,
     (*else, easy*)
     Print["case 2"];
     anext = Select[aset, # < amax &];
     mnext = Select[Mset, # > amax &] - amax;
     path = Flatten[{amax, findpath[anext, mnext]}];
     ],
    If[MemberQ[Mset, amax],
     Print["case 3"];
     mprime = Select[Mset, # != mM &] - amax;
     anext = Select[aset, # < amax &];
     Print[anext, mprime];
     tpath = findpath[anext, mprime];
     Print[tpath];
     path = Insert[tpath, amax, 2];,
     Print["case 4"];
     mprime = Select[Mset, # != mM &] - amax;
     anext = Select[aset, # < amax &];
     Print[anext, mprime];
     tpath = findpath[anext, mprime];
     Print[tpath];
     parsum = amax;
     k = 1;
     t = 0;
     Do[parsum = ai + parsum;
      If[parsum == mM, t = 1; Print["break", parsum]; Break[]];
      k = k + 1;, {ai, tpath}];
     If[t == 1,
      path =
        Flatten[{tpath[[k]],
          Insert[Delete[tpath, k], amax, k + 1]}];,
      path = Flatten[{amax, tpath}];];
     ]
    ]
   ];
  path
  ]