import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } void main() { try { for (; ; ) { const N = readInt(); const X = readLong(); auto A = new long[N]; foreach (i; 0 .. N) { A[i] = readLong(); } auto ASum = new long[N + 1]; foreach (i; 0 .. N) { ASum[i + 1] = ASum[i] + A[i]; } auto ls = new int[N + 1]; auto rs = new int[N + 1]; foreach (i; 0 .. N + 1) { ls[i] = ASum.upperBound(ASum[i] + X); rs[i] = ASum.lowerBound(ASum[i] - X); } debug { writeln("A = ", A); writeln("ls = ", ls); writeln("rs = ", rs); } auto dp0 = new int[][](N + 1, N + 2); auto dp1 = new int[][](N + 1, N + 2); bool check0(int i, int ja, int jb) { return (dp0[i][jb] - dp0[i][ja] < jb - ja); } bool check1(int j, int ia, int ib) { return (dp1[j][ib] - dp1[j][ia] < ib - ia); } foreach (w; 2 .. N + 1) { foreach (i; 0 .. N - w + 1) { const j = i + w; int x; // [i, i + 1), ..., [i, ls[i] - 1) if (check0(i, i + 1, min(ls[i], j))) { x = 1; } // [rs[j], j), ..., [j - 1, j) if (check1(j, max(rs[j], i + 1), j)) { x = 1; } debug { writeln(i, " ", j, ": ", x); } dp0[i][j + 1] = dp0[i][j] + x; dp1[j][i] = dp1[j][i + 1] + x; } } const ans = dp0[0][N + 1] - dp0[0][N]; writeln(ans ? "A" : "B"); } } catch (EOFException e) { } }