/+ dub.sdl:
    name "F"
    dependency "dunkelheit" version="1.0.1"
+/

import std.stdio, std.algorithm, std.range, std.conv;
// import dkh.foundation, dkh.scanner;

int n, use;
long mod;

int[] upn, up2n;

int[] pos, psm;

long[][] memo;
bool[][] vis;
static this() {
    memo = new long[][](510, 260);
}

long calc(int id, int a) {
    if (id == 2 * n) {
        if (a == use) return 1;
        return 0;
    }

    if (vis[id][a]) return memo[id][a];
    vis[id][a] = true;

    int p = pos[id];

    long ans = 0;

    if (p < n) {
        // inside
        {
            //not use
            long freq = up2n[p] - n - (id - psm[id]) - (use - a);
            if (freq > 0) ans += freq * calc(id + 1, a);
        }
        if (a + 1 <= use) {
            //use
            long freq = upn[p] - psm[id] - a;
            if (freq > 0) ans += freq * calc(id + 1, a + 1);
        }
    } else {
        // outside
        long freq = up2n[p] - psm[id] - a;
        if (freq > 0) ans += freq * calc(id + 1, a);
    }
    ans = ((ans % mod) + mod) % mod;
    return memo[id][a] = ans;
}

int main() {
    Scanner sc = new Scanner(stdin);
    scope(exit) assert(!sc.hasNext);

    sc.read(n, mod);

    upn = new int[2 * n];
    up2n = new int[2 * n];

    foreach (i; 0..2 * n) {
        foreach (j; 0..2 * n) {
            long z = i * i + j * j;
            if (z < n * n) upn[i]++;
            if (z <= 4 * n * n) up2n[i]++;
        }
    }

    pos = iota(2 * n).array;
    pos.sort!((a, b){
        int ap = (a < n) ? upn[a] : up2n[a];
        int bp = (b < n) ? upn[b] : up2n[b];
        if (ap != bp) return ap < bp;
        return a > b;
    });

//    writeln(pos);

    psm = new int[2 * n + 1];
    foreach (i; 0..2 * n) {
        psm[i + 1] = psm[i];
        if (pos[i] >= n) psm[i + 1]++;
    }

/*    writeln(upn);
    writeln(up2n);
    writeln(pos);
    writeln(psm);*/
    long ans = 0;
    foreach (_use; 0..n + 1) {
        use = _use;

        vis = new bool[][](510, 260);
        if (use % 2 == 0) {
            ans += calc(0, 0);
        } else {
            ans -= calc(0, 0);
        }
        ans = ((ans % mod) + mod) % mod;
    }

    writeln(ans);

    return 0;
}
/* IMPORT /home/yosupo/Programs/dunkelheit/source/dkh/foundation.d */
 
// module dkh.foundation;

 
static if (__VERSION__ <= 2070) {
    /*
    Copied by https://github.com/dlang/phobos/blob/master/std/algorithm/iteration.d
    Copyright: Andrei Alexandrescu 2008-.
    License: $(HTTP boost.org/LICENSE_1_0.txt, Boost License 1.0).
    */
    template fold(fun...) if (fun.length >= 1) {
        auto fold(R, S...)(R r, S seed) {
            import std.algorithm : reduce;
            static if (S.length < 2) {
                return reduce!fun(seed, r);
            } else {
                import std.typecons : tuple;
                return reduce!fun(tuple(seed), r);
            }
        }
    }
     
}
/* IMPORT /home/yosupo/Programs/dunkelheit/source/dkh/container/stackpayload.d */
// module dkh.container.stackpayload;

 
struct StackPayload(T, size_t MINCAP = 4) if (MINCAP >= 1) {
    import core.exception : RangeError;

    private T* _data;
    private uint len, cap;

    @property bool empty() const { return len == 0; }
    @property size_t length() const { return len; }
    alias opDollar = length;

     
    inout(T)[] data() inout { return (_data) ? _data[0..len] : null; }
    
    ref inout(T) opIndex(size_t i) inout {
        version(assert) if (len <= i) throw new RangeError();
        return _data[i];
    }  
    ref inout(T) front() inout { return this[0]; }  
    ref inout(T) back() inout { return this[$-1]; }  

    void reserve(size_t newCap) {
        import core.memory : GC;
        import core.stdc.string : memcpy;
        import std.conv : to;
        if (newCap <= cap) return;
        void* newData = GC.malloc(newCap * T.sizeof);
        cap = newCap.to!uint;
        if (len) memcpy(newData, _data, len * T.sizeof);
        _data = cast(T*)(newData);
    }  
    void free() {
        import core.memory : GC;
        GC.free(_data);
    }  
     
    void clear() {
        len = 0;
    }

    void insertBack(T item) {
        import std.algorithm : max;
        if (len == cap) reserve(max(cap * 2, MINCAP));
        _data[len++] = item;
    }  
    alias opOpAssign(string op : "~") = insertBack;  
    void removeBack() {
        assert(!empty, "StackPayload.removeBack: Stack is empty");
        len--;
    }  
}

 
/* IMPORT /home/yosupo/Programs/dunkelheit/source/dkh/scanner.d */
// module dkh.scanner;

// import dkh.container.stackpayload;

 
class Scanner {
    import std.stdio : File;
    import std.conv : to;
    import std.range : front, popFront, array, ElementType;
    import std.array : split;
    import std.traits : isSomeChar, isStaticArray, isArray; 
    import std.algorithm : map;
    private File f;
     
    this(File f) {
        this.f = f;
    }
    private char[512] lineBuf;
    private char[] line;
    private bool succW() {
        import std.range.primitives : empty, front, popFront;
        import std.ascii : isWhite;
        while (!line.empty && line.front.isWhite) {
            line.popFront;
        }
        return !line.empty;
    }
    private bool succ() {
        import std.range.primitives : empty, front, popFront;
        import std.ascii : isWhite;
        while (true) {
            while (!line.empty && line.front.isWhite) {
                line.popFront;
            }
            if (!line.empty) break;
            line = lineBuf[];
            f.readln(line);
            if (!line.length) return false;
        }
        return true;
    }

    private bool readSingle(T)(ref T x) {
        import std.algorithm : findSplitBefore;
        import std.string : strip;
        import std.conv : parse;
        if (!succ()) return false;
        static if (isArray!T) {
            alias E = ElementType!T;
            static if (isSomeChar!E) {
                 
                 
                auto r = line.findSplitBefore(" ");
                x = r[0].strip.dup;
                line = r[1];
            } else static if (isStaticArray!T) {
                foreach (i; 0..T.length) {
                    assert(succW());
                    x[i] = line.parse!E;
                }
            } else {
                StackPayload!E buf;
                while (succW()) {
                    buf ~= line.parse!E;
                }
                x = buf.data;
            }
        } else {
            x = line.parse!T;
        }
        return true;
    }

     
    int unsafeRead(T, Args...)(ref T x, auto ref Args args) {
        if (!readSingle(x)) return 0;
        static if (args.length == 0) {
            return 1;
        } else {
            return 1 + read(args);
        }
    }
     
    void read(Args...)(auto ref Args args) {
        import std.exception : enforce;
        static if (args.length != 0) {
            enforce(readSingle(args[0]));
            read(args[1..$]);
        }
    }
     
    bool hasNext() {
        return succ();
    }
}


 
 

 

/*
This source code generated by dunkelheit and include dunkelheit's source code.
dunkelheit's Copyright: Copyright (c) 2016- Kohei Morita. (https://github.com/yosupo06/dunkelheit)
dunkelheit's License: MIT License(https://github.com/yosupo06/dunkelheit/blob/master/LICENSE.txt)
*/


Measured memory_bytes: 12796