from itertools import*
E=enumerate
L=len
U=lambda x:{L(x)-i:a for i,a in E(x,1)}
V=eval
def G(v,r=[]):
 if[]==v:yield r;return
 for k in product(*([[-1,0,1]]*L(v[0]))):N=[a+b for a,b in zip(v[0],k)];yield from G(v[1:],r+[[[-1]+N[1:]],[N]][N[0]!=0])
def P(p):
 if[]==p:return{0:1}
 s=U(p[0])
 for e in p[1:]:
  n={}
  for i,a in E(e,1):
   for A in s:n[j]=n.get(j:=A+L(e)-i,0)+s[A]*a
  s=n
 return s
def f(n,d):
 S,D,M={*map(str,d)},[],{}
 for i in S:Y=d.count(V(i));D+=[(i,Y)]+[(i,1)]*(Y>1==L(S));M[i]=max(Y,M.get(i,0))
 N=U(n);q,O=[[(a,b,t:=P([V(i)for J,K in[(j,M[j])for j in{*M}-{a}]+[(a,M[a]-b)]*(M[a]>b)for i in[J]*K]),[1]+[0]*(max(N)-max(t)))for a,b in D]],[]
 while q:
  a=q.pop(0);O+=a,;r={}
  for *_,p,o in a:
   for A,B in P([[*p.values()],o]).items():r[A]=r.get(A,0)+B
  if r==N:return[[i[-1],[V(i[0])]*int(i[1])]for i in a]
  for i in G([j[-1]for j in a]):v=[(A,B,C,z)for(A,B,C,_),z in zip(a,i)];q+=-~-(v in O)*[v]
 
print(f([1,4], [[1,3], [1,2]]))
print(f([1,4], [[1,3], [1,3]]))
print(f([2,-1,4], [[1,0], [1,0,4]]))

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