import std.stdio, std.conv, std.functional, std.string;
import std.algorithm, std.array, std.container, std.range, std.typecons;
import std.bigint, std.numeric, std.math, std.random;
import core.bitop;

string FMT_F = "%.10f";

static File _f;
void file_io(string fn) { _f = File(fn, "r"); }
static string[] s_rd;
T _RD(T = long)() { while(!s_rd.length) s_rd = readln.chomp.split; string res = s_rd[0]; s_rd.popFront; return res.to!T; }
T _RD(T = long)(File f) { while(!s_rd.length) s_rd = f.readln.chomp.split; string res = s_rd[0]; s_rd.popFront; return res.to!T; }
T[] _RDA(T = long)(T fix = 0) { auto r = readln.chomp.split.to!(T[]); r[] += fix; return r; }
T[] _RDA(T = long)(File f, T fix = 0) { auto r = f.readln.chomp.split.to!(T[]); r[] += fix; return r; }
T RD(T = long)() { if (_f.isOpen) return _RD!T(_f); else return _RD!T; }
T[] RDA(T = long)(T fix = 0) { if (_f.isOpen)  return _RDA!T(_f, fix); else return _RDA!T(fix); }

size_t[] MAKE_IDX(alias less = "a < b", Range)(Range range) { auto idx = new size_t[](range.length); makeIndex!(less)(range, idx); return idx;}
size_t MIN_POS(alias less = "a < b", Range)(Range range) { auto r = minPos!(less)(range); return range.length - r.length; }

void chmin(T)(ref T x, T y) { x = min(x, y); } void chmax(T)(ref T x, T y) { x = max(x, y); }
bool inside(T)(T x, T b, T e) { return x >= b && x < e; }
T lcm(T)(T x, T y) { return x * (y / gcd(x, y)); }

long mod = 10^^9 + 7;
//long mod = 998_244_353;
//long mod = 1_000_003;
void moda(ref long x, long y) { x = (x + y) % mod; }
void mods(ref long x, long y) { x = ((x + mod) - (y % mod)) % mod; }
void modm(ref long x, long y) { x = (x * y) % mod; }
void modpow(ref long x, long y) { if (!y) { x = 1; return; } auto t = x; x.modpow(y>>1); x.modm(x); if (y&1) x.modm(t); }
void modd(ref long x, long y) { y.modpow(mod - 2); x.modm(y); }

T binarySearch(alias pred, T)(T ok, T ng)
{ 
	while (abs(ok-ng) > 1)
	{
		auto mid = (ok+ng)/2;
		if (unaryFun!pred(mid)) ok = mid;
		else ng = mid;
	}
	return ok;
}

void main()
{
	auto T = RD;
	auto ans = new long[](T);
	foreach (ti; 0..T)
	{
		auto N = RD;
		auto A = RD;
		auto W = RD;
		auto K = RD;

		if (A < K-1 && W < N+1-K)
			ans[ti] = -1;
		else if (N != K)
			ans[ti] = (A-1) / K;
		else
		{
			auto cnt = (W+N) / N;
			auto rem = W % N;
			auto w1 = cnt*(cnt+1)/2;
			auto w2 = cnt*(cnt-1)/2;
			auto B = A - (w1 * rem + w2 * (N - rem));
			
			if (A >= rem-1)
				ans[ti] = (B-1) / K;
			else
			{
				auto ww = cnt+1;
				auto w = (W-ww+(N-1)) / (N-1);
				auto rem2 = (W-ww) % (N-1);
				auto v1 = cnt*(cnt+1)/2;
				auto v2 = cnt*(cnt-1)/2;
				auto C = v1 * rem2 + v2 * (N - 1 - rem2);
				bool f(long x)
				{
					auto D = ((A-x) - C + N - 2) / (N-1);
					return x + ww*(ww+1)/2 < D;
				}
				auto r = binarySearch!(f)(0, A+1);
				ans[ti] = r + ww*(ww+1)/2;
			}
		}
	}

	foreach (e; ans)
		writeln(e == -1 ? ":(" : e.to!string);
	stdout.flush;
	debug readln;
}