import sys
readline=sys.stdin.readline

T=int(readline())
for t in range(T):
    N,A,W,K=map(int,readline().split())
    if K-1<=A or N-K+1<=W:
        if K<N:
            ans=(A-(K-1))//K
        else:
            if W%N==0:
                if A>=K-1:
                    ans=-(W//N)*(W//N+1)//2+(A-(K-1))//K
                else:
                    ans=-(W//N)*(W//N+1)//2+min(-(W//N+1)+A,0)
            else:
                if W%N*(W//N+1)<=A:
                    A-=W%N*(W//N+1)
                    if A>=K-1:
                        ans=-(W//N)*(W//N+1)//2+(A-(K-1))//K
                    else:
                        ans=-(W//N)*(W//N+1)//2+min(-(W//N+1)+A,0)
                else:
                    if A>=K-1:
                        ans=-(W//N+1)*(W//N+2)//2+(A-(K-1))//K
                    else:
                        ans=-(W//N+1)*(W//N+2)//2+min(-(W//N+1)+A,0)
    else:
        ans=":("
    print(ans)