package adv2020; import java.io.*; import java.util.ArrayDeque; import java.util.Arrays; import java.util.InputMismatchException; import java.util.Queue; // まだ途中 public class Day6 { InputStream is; FastWriter out; // String INPUT = "5 3 2 1"; // String INPUT = "7 8 0 2"; // String INPUT = "7 8 6 0"; // String INPUT = "13 9 4 5"; String INPUT = ""; // 0 0 0 6 7 8 8 public void solve() { while(!eof())go(); } // a+(a+1)+..+(a+b-1) long sum(long a, long b) { return a*b+(b-1)*b/2; } // a+(a-1)+..+(a-b+1) long sumr(long a, long b) { return a*b-(b-1)*b/2; } void go() { int n = ni(); long P = nl(), X = nl(), Y = nl(); int h = n/2; if(X > Y){ if(n >= 7){ if(X < P) { long ans = -1; for(int F = 2;F <= h;F++){ long S = F*Y; int num = h+1-F; int hnum = h; for(long x = P;x > X && hnum > 0;x--){ int des = Math.min(hnum, F-1); S += x*des; hnum -= des; } if(hnum >= F-1)continue; num += hnum; for(long x = X;x >= 0 && num > 0;x--){ if(x == Y)continue; int des = Math.min(num, F-1); S += x*des; num -= des; } if(num > 0)continue; // tr(S, F); ans = Math.max(ans, S); } out.println(ans); return; }else{ out.println(-1); return; } }else if(n == 5){ // 0 0 2 2 3 if(X < P-1){ out.println(Y+Y+X+P-1+P); return; }else if(X == P-1) { if(2*Y >= X){ // 2,2,1 out.println(Y*4+P); return; }else{ out.println(-1); return; } }else{ out.println(-1); return; } }else if(n == 3){ // [0,Y], X-Y+[X-Y+1,M-Y] if(X < P && Math.max(0, X-Y+X-Y+1) <= Math.min(Y, X-Y+P-Y)){ out.println(3*Y); return; }else{ out.println(-1); return; } }else if(n == 1){ out.println(-1); return; } assert false; }else if(X == Y){ out.println(Y*(h+1) + P*h); return; }else if(X < Y){ long ans = -1; for(int F = 2;F <= h;F++){ // XがLに属する場合 // F*Lしかないのかな? { int L = (h+1+F-1)/F; int rem = n - F*L; if(X >= L-1) { outer: for (int H = 1; F * H <= rem; H++) { int hrem = rem - F * H; if (hrem < 0) continue; int h1 = hrem / (F - 1); int hr1 = hrem % (F - 1); int hh = H + h1 + (hr1 > 0 ? 1 : 0); if (P - (X + 1) + 1 < hh) continue; long lbal = sum(Y - X, L); // H側の最小バランス long hbalmin = sum(X + 1 - Y, H); long hbalmax = sumr(P - Y, H); // 00000111166666888 if (hbalmin <= lbal && lbal <= hbalmax) { long lbalst = lbal; long hbalst = sumr(P - Y - (hh - H), H); // tr(F, L, H, lbalst, hbalmin, hbalmax, hbalst); // tr(lbalst, hbalst); long S = Y * (H + L) * F; S += (F - 1) * sumr(P, h1) + hr1 * (P - h1); if (lbalst <= hbalst) { // 安定な場合 ans = Math.max(ans, S); // tr(S); } else { if (hr1 > 0) { // hr1をH回移動できる long hbalst2 = hbalst + H; if (lbalst <= hbalst2) { S -= (lbalst - hbalst) * hr1; ans = Math.max(ans, S); // tr(S); continue outer; }else{ S -= H*hr1; } hbalst = hbalst2; } // F-1をたくさん移動できる S -= (lbalst - hbalst) * (F - 1); // tr(S); ans = Math.max(ans, S); } } } } } for(int L = 1;F*L <= h+1;L++){ for(int H = 1;F*H <= h+1;H++){ // XがどちらのFでもない場合 outer: { int hrem = h - F*H; if(hrem < 0)break outer; int h1 = hrem / (F-1); int hr1 = hrem % (F-1); // H側の合計高さ int hh = H + h1 + (hr1 > 0 ? 1 : 0); if(P-X+1 < hh)break outer; if(P-X+1 == hh){ // やっかい // tr(F, H, L); }else{ int lrem = h+1 - F*L; if(lrem < 0)break outer; int l1 = lrem / (F-1); int lr1 = lrem % (F-1); // L側の合計高さ int lh = L + l1 + (lr1 > 0 ? 1 : 0); if(X-0+1 < lh)break outer; // L側の最小バランス long lbalmin = sum(Y-X, L); long lbalmax = sumr(Y, L); // H側の最小バランス long hbalmin = sum(X+1-Y, H); long hbalmax = sumr(P-Y, H); // tr(lbalmin, lbalmax, hbalmin, hbalmax); // tr(F, L, H, lh, hh, l1, h1); // 00000111166666888 if (Math.max(lbalmin, hbalmin) <= Math.min(lbalmax, hbalmax)) { long lbalst = sum(Y-X+(lh-L), L); long hbalst = sumr(P-Y-(hh-H), H); // tr(F, L, H, lbalmin, lbalmax, lbalst, hbalmin, hbalmax, hbalst); long S = Y*(H+L)*F; S += (F-1)*sumr(X, l1) + lr1*(X-l1); S += (F-1)*sumr(P, h1) + hr1*(P-h1); if(lbalst <= hbalst){ // 安定な場合 ans = Math.max(ans, S); // tr(S); }else { // LまたはHを削り出す // tr(lbalmin, lbalmax, lbalst, hbalmin, hbalmax, hbalst); // tr("YABAI", F, L, H); if(lr1 > hr1) { if (hr1 > 0) { // hr1をH回移動できる long hbalst2 = hbalst + H; if (lbalst <= hbalst2) { S -= (lbalst - hbalst) * hr1; ans = Math.max(ans, S); break outer; }else{ S -= H*hr1; } hbalst = hbalst2; } if (lr1 > 0) { // lr1をL回移動できる long lbalst2 = lbalst - L; if (lbalst2 <= hbalst) { S -= (lbalst - hbalst) * lr1; ans = Math.max(ans, S); break outer; }else{ S -= L*lr1; } lbalst = lbalst2; } }else{ // 13 9 4 5 // 6 1 6 // 2 2 2 3 3 3 4 7 7 7 8 9 9 // tr(F, H, L, h1, hr1, l1, lr1, lbalst, hbalst); if (lr1 > 0) { // lr1をL回移動できる long lbalst2 = lbalst - L; if (lbalst2 <= hbalst) { S -= (lbalst - hbalst) * lr1; ans = Math.max(ans, S); break outer; }else{ S -= L*lr1; } lbalst = lbalst2; } if (hr1 > 0) { // hr1をH回移動できる long hbalst2 = hbalst + H; if (lbalst <= hbalst2) { S -= (lbalst - hbalst) * hr1; ans = Math.max(ans, S); break outer; }else{ S -= H*hr1; } hbalst = hbalst2; } } // F-1をたくさん移動できる S -= (lbalst - hbalst) * (F-1); ans = Math.max(ans, S); } }else{ break outer; } } } } } inner: { long S = Y*F; int lrem = h+1; for(long t = X;t >= 0 && lrem > 0;t--){ int de = Math.min(lrem, F-1); S += t*de; lrem -= de; } if(lrem > 0)break inner; int hrem = h-F; for(long t = P;t >= Y+1 && hrem > 0;t--){ int de = Math.min(hrem, F-1); S += t*de; hrem -= de; } if(hrem > 0)break inner; ans = Math.max(ans, S); } } // F = 1 if(X-h >= 0 && X+h <= P){ // X-h X-h+1 ... X long lmax = X*(X+1)/2 - (X-h-1)*(X-h)/2; long lmin = X + h*(h-1)/2; long hmax = P*(P+1)/2 - (P-h+1)*(P-h)/2; long hmin = (X+h)*(X+h+1)/2 - X*(X+1)/2; // tr(lmin, lmax, hmin, hmax); if(lmin + hmin <= n*Y && n*Y <= lmax + hmax) { ans = Math.max(ans, n * Y); } } out.println(ans); return; } } public static void main(String[] args) { new Day6().run(); } public void run() { long S = System.currentTimeMillis(); is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new FastWriter(System.out); solve(); out.flush(); long G = System.currentTimeMillis(); tr(G-S+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } private boolean eof() { if(lenbuf == -1)return true; int lptr = ptrbuf; while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false; try { is.mark(1000); while(true){ int b = is.read(); if(b == -1){ is.reset(); return true; }else if(!isSpaceChar(b)){ is.reset(); return false; } } } catch (IOException e) { return true; } } private final byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } // private boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } private int ni() { int num = 0, b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } public static class FastWriter { private static final int BUF_SIZE = 1<<13; private final byte[] buf = new byte[BUF_SIZE]; private final OutputStream out; private int ptr = 0; private FastWriter(){out = null;} public FastWriter(OutputStream os) { this.out = os; } public FastWriter(String path) { try { this.out = new FileOutputStream(path); } catch (FileNotFoundException e) { throw new RuntimeException("FastWriter"); } } public FastWriter write(byte b) { buf[ptr++] = b; if(ptr == BUF_SIZE)innerflush(); return this; } public FastWriter write(char c) { return write((byte)c); } public FastWriter write(char[] s) { for(char c : s){ buf[ptr++] = (byte)c; if(ptr == BUF_SIZE)innerflush(); } return this; } public FastWriter write(String s) { s.chars().forEach(c -> { buf[ptr++] = (byte)c; if(ptr == BUF_SIZE)innerflush(); }); return this; } private static int countDigits(int l) { if (l >= 1000000000) return 10; if (l >= 100000000) return 9; if (l >= 10000000) return 8; if (l >= 1000000) return 7; if (l >= 100000) return 6; if (l >= 10000) return 5; if (l >= 1000) return 4; if (l >= 100) return 3; if (l >= 10) return 2; return 1; } public FastWriter write(int x) { if(x == Integer.MIN_VALUE){ return write((long)x); } if(ptr + 12 >= BUF_SIZE)innerflush(); if(x < 0){ write((byte)'-'); x = -x; } int d = countDigits(x); for(int i = ptr + d - 1;i >= ptr;i--){ buf[i] = (byte)('0'+x%10); x /= 10; } ptr += d; return this; } private static int countDigits(long l) { if (l >= 1000000000000000000L) return 19; if (l >= 100000000000000000L) return 18; if (l >= 10000000000000000L) return 17; if (l >= 1000000000000000L) return 16; if (l >= 100000000000000L) return 15; if (l >= 10000000000000L) return 14; if (l >= 1000000000000L) return 13; if (l >= 100000000000L) return 12; if (l >= 10000000000L) return 11; if (l >= 1000000000L) return 10; if (l >= 100000000L) return 9; if (l >= 10000000L) return 8; if (l >= 1000000L) return 7; if (l >= 100000L) return 6; if (l >= 10000L) return 5; if (l >= 1000L) return 4; if (l >= 100L) return 3; if (l >= 10L) return 2; return 1; } public FastWriter write(long x) { if(x == Long.MIN_VALUE){ return write("" + x); } if(ptr + 21 >= BUF_SIZE)innerflush(); if(x < 0){ write((byte)'-'); x = -x; } int d = countDigits(x); for(int i = ptr + d - 1;i >= ptr;i--){ buf[i] = (byte)('0'+x%10); x /= 10; } ptr += d; return this; } public FastWriter write(double x, int precision) { if(x < 0){ write('-'); x = -x; } x += Math.pow(10, -precision)/2; // if(x < 0){ x = 0; } write((long)x).write("."); x -= (long)x; for(int i = 0;i < precision;i++){ x *= 10; write((char)('0'+(int)x)); x -= (int)x; } return this; } public FastWriter writeln(char c){ return write(c).writeln(); } public FastWriter writeln(int x){ return write(x).writeln(); } public FastWriter writeln(long x){ return write(x).writeln(); } public FastWriter writeln(double x, int precision){ return write(x, precision).writeln(); } public FastWriter write(int... xs) { boolean first = true; for(int x : xs) { if (!first) write(' '); first = false; write(x); } return this; } public FastWriter write(long... xs) { boolean first = true; for(long x : xs) { if (!first) write(' '); first = false; write(x); } return this; } public FastWriter writeln() { return write((byte)'\n'); } public FastWriter writeln(int... xs) { return write(xs).writeln(); } public FastWriter writeln(long... xs) { return write(xs).writeln(); } public FastWriter writeln(char[] line) { return write(line).writeln(); } public FastWriter writeln(char[]... map) { for(char[] line : map)write(line).writeln(); return this; } public FastWriter writeln(String s) { return write(s).writeln(); } private void innerflush() { try { out.write(buf, 0, ptr); ptr = 0; } catch (IOException e) { throw new RuntimeException("innerflush"); } } public void flush() { innerflush(); try { out.flush(); } catch (IOException e) { throw new RuntimeException("flush"); } } public FastWriter print(byte b) { return write(b); } public FastWriter print(char c) { return write(c); } public FastWriter print(char[] s) { return write(s); } public FastWriter print(String s) { return write(s); } public FastWriter print(int x) { return write(x); } public FastWriter print(long x) { return write(x); } public FastWriter print(double x, int precision) { return write(x, precision); } public FastWriter println(char c){ return writeln(c); } public FastWriter println(int x){ return writeln(x); } public FastWriter println(long x){ return writeln(x); } public FastWriter println(double x, int precision){ return writeln(x, precision); } public FastWriter print(int... xs) { return write(xs); } public FastWriter print(long... xs) { return write(xs); } public FastWriter println(int... xs) { return writeln(xs); } public FastWriter println(long... xs) { return writeln(xs); } public FastWriter println(char[] line) { return writeln(line); } public FastWriter println(char[]... map) { return writeln(map); } public FastWriter println(String s) { return writeln(s); } public FastWriter println() { return writeln(); } } public static void trnz(int... o) { for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" "); System.out.println(); } // print ids which are 1 public static void trt(long... o) { Queue stands = new ArrayDeque<>(); for(int i = 0;i < o.length;i++){ for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x)); } System.out.println(stands); } public static void tf(boolean... r) { for(boolean x : r)System.out.print(x?'#':'.'); System.out.println(); } public static void tf(boolean[]... b) { for(boolean[] r : b) { for(boolean x : r)System.out.print(x?'#':'.'); System.out.println(); } System.out.println(); } public void tf(long[]... b) { if(INPUT.length() != 0) { for (long[] r : b) { for (long x : r) { for (int i = 0; i < 64; i++) { System.out.print(x << ~i < 0 ? '#' : '.'); } } System.out.println(); } System.out.println(); } } public void tf(long... b) { if(INPUT.length() != 0) { for (long x : b) { for (int i = 0; i < 64; i++) { System.out.print(x << ~i < 0 ? '#' : '.'); } } System.out.println(); } } private void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); } }