```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline

_cpp_source = """
#include <torch/extension.h>
torch::Tensor exclusive_scan_cuda(torch::Tensor x);
"""

_cuda_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_runtime.h>
#include <cub/cub.cuh>

constexpr int THREADS = 256;
constexpr int ITEMS = 16;
constexpr int TILE = THREADS * ITEMS;

__global__ void tile_sums_kernel(
    const float* __restrict__ x,
    float* __restrict__ sums,
    int64_t columns,
    int64_t tiles,
    int64_t total_tiles)
{
    using Reduce = cub::BlockReduce<float, THREADS>;
    __shared__ typename Reduce::TempStorage storage;

    for (int64_t tile_id = blockIdx.x;
         tile_id < total_tiles;
         tile_id += gridDim.x) {
        const int64_t row = tile_id / tiles;
        const int64_t tile = tile_id % tiles;
        const int64_t start = tile * TILE;
        const float* input = x + row * columns;

        float sum = 0.0f;
        #pragma unroll
        for (int i = 0; i < ITEMS; ++i) {
            const int64_t column = start + threadIdx.x + i * THREADS;
            if (column < columns)
                sum += input[column];
        }

        const float total = Reduce(storage).Sum(sum);
        if (threadIdx.x == 0)
            sums[tile_id] = total;
        __syncthreads();
    }
}

__global__ void scan_tiles_kernel(
    const float* __restrict__ x,
    const float* __restrict__ sums,
    float* __restrict__ output,
    int64_t columns,
    int64_t tiles,
    int64_t total_tiles)
{
    using Load = cub::BlockLoad<
        float, THREADS, ITEMS, cub::BLOCK_LOAD_WARP_TRANSPOSE>;
    using Scan = cub::BlockScan<
        float, THREADS, cub::BLOCK_SCAN_WARP_SCANS>;
    using Store = cub::BlockStore<
        float, THREADS, ITEMS, cub::BLOCK_STORE_WARP_TRANSPOSE>;

    __shared__ union {
        typename Load::TempStorage load;
        typename Scan::TempStorage scan;
        typename Store::TempStorage store;
    } storage;
    __shared__ float prefix;

    for (int64_t tile_id = blockIdx.x;
         tile_id < total_tiles;
         tile_id += gridDim.x) {
        const int64_t row = tile_id / tiles;
        const int64_t tile = tile_id % tiles;
        const int64_t start = tile * TILE;
        const int valid = static_cast<int>(
            columns - start < TILE ? columns - start : TILE);

        if (threadIdx.x == 0) {
            float offset = 0.0f;
            for (int64_t t = 0; t < tile; ++t)
                offset += sums[row * tiles + t];
            prefix = offset;

            if (tile == 0)
                output[row * (columns + 1)] = 0.0f;
        }

        float values[ITEMS];
        Load(storage.load).Load(
            x + row * columns + start, values, valid, 0.0f);
        __syncthreads();

        Scan(storage.scan).InclusiveSum(values, values);
        __syncthreads();

        #pragma unroll
        for (int i = 0; i < ITEMS; ++i)
            values[i] += prefix;

        Store(storage.store).Store(
            output + row * (columns + 1) + start + 1,
            values,
            valid);
        __syncthreads();
    }
}

torch::Tensor exclusive_scan_cuda(torch::Tensor x)
{
    TORCH_CHECK(x.is_cuda(), "Expected a CUDA tensor");
    TORCH_CHECK(x.scalar_type() == at::kFloat, "Expected float32");
    TORCH_CHECK(x.dim() == 2 && x.is_contiguous(),
                "Expected a contiguous two-dimensional tensor");
    TORCH_CHECK(x.size(1) > 0, "Scan dimension must be nonempty");

    const c10::cuda::CUDAGuard guard(x.device());

    // Preserve the original expression: [:-1] slices dimension zero.
    const int64_t rows = x.size(0) > 0 ? x.size(0) - 1 : 0;
    const int64_t columns = x.size(1);
    auto output = torch::empty({rows, columns + 1}, x.options());

    if (rows == 0)
        return output;

    const int64_t tiles = (columns + TILE - 1) / TILE;
    const int64_t total_tiles = rows * tiles;
    auto sums = torch::empty({rows, tiles}, x.options());

    const int blocks = static_cast<int>(
        total_tiles < 65535 ? total_tiles : 65535);
    const auto stream = at::cuda::getCurrentCUDAStream();

    tile_sums_kernel<<<blocks, THREADS, 0, stream>>>(
        x.data_ptr<float>(),
        sums.data_ptr<float>(),
        columns,
        tiles,
        total_tiles);
    C10_CUDA_KERNEL_LAUNCH_CHECK();

    scan_tiles_kernel<<<blocks, THREADS, 0, stream>>>(
        x.data_ptr<float>(),
        sums.data_ptr<float>(),
        output.data_ptr<float>(),
        columns,
        tiles,
        total_tiles);
    C10_CUDA_KERNEL_LAUNCH_CHECK();

    return output;
}
"""

_scan_extension = load_inline(
    name="fused_exclusive_cumsum_cuda_v1",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["exclusive_scan_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(self, dim):
        super().__init__()
        self.dim = dim

    def forward(self, x):
        if (
            x.is_cuda
            and x.dtype == torch.float32
            and x.ndim == 2
            and self.dim in (1, -1)
            and x.shape[1] > 0
            and x.is_contiguous()
        ):
            return _scan_extension.exclusive_scan_cuda(x)

        exclusive_cumsum = torch.cat(
            (
                torch.zeros_like(
                    x.select(self.dim, 0).unsqueeze(self.dim)
                ),
                x,
            ),
            dim=self.dim,
        )[:-1]
        return torch.cumsum(exclusive_cumsum, dim=self.dim)
```